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<ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="inerz">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="1">M</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="671" left="198" top="504" width="84.75" height="15" align-x="198" align-y="516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Forza d'inerzia </text> </region> <region region-id="306" left="6" top="552" width="138.75" height="15" align-x="6" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Times New Roman" charset="0" size="14"> Condizioni al contorno: </f> </text> </region> <region region-id="12" left="6" top="582" width="69" height="15" align-x="9.75" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Times New Roman" charset="0" size="14"> in x = 0 </f> </text> </region> <region region-id="18" left="6" top="612.75" width="73.5" height="15.75" align-x="38.25" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:symResult> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="13"/> </region> <region region-id="21" left="6" top="648.75" width="151.5" height="15.75" align-x="95.25" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y'</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="14"/> </region> <region region-id="26" left="6" top="702" width="71.25" height="15" align-x="9.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Times New Roman" charset="0" size="14"> in x = l </f> </text> </region> <region region-id="430" left="6" top="727.5" width="391.5" height="21" align-x="95.25" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y''</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="15"/> </region> <region region-id="673" left="6" top="763.5" width="1122" height="25.5" align-x="194.25" align-y="780" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="inerz">F</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="16"/> </region> <region region-id="316" left="6" top="816" width="398.25" height="15" align-x="29.25" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Riassunto delle condizioni al contorno (che formano un sistema lineare) </text> </region> <region region-id="42" left="6" top="852.75" width="54" height="15.75" align-x="44.25" align-y="864" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="41" left="6" top="876.75" width="53.25" height="15.75" align-x="43.5" align-y="888" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="18"/> </region> <region region-id="436" left="6" top="900.75" width="288" height="15.75" align-x="278.25" align-y="912" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="19"/> </region> <region region-id="612" left="6" top="931.5" width="946.5" height="25.5" align-x="936.75" align-y="948" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="20"/> </region> <region region-id="674" left="900" top="962.25" width="234" height="18.75" align-x="904.5" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> in questa equazione si può semplificare β<f family="Times New Roman" charset="0" size="14"> <inlineAttr font-weight="normal" underline="false" line-through="false"> <c val="#f00"> 3 </c> </inlineAttr> </f> </text> </region> <region region-id="320" left="6" top="1002" width="250.5" height="15" align-x="6" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Poniamo per semplicità: α = β l e otteniamo: </text> </region> <region region-id="49" left="6" top="1032.75" width="54" height="15.75" align-x="44.25" align-y="1044" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="21"/> </region> <region region-id="50" left="6" top="1056.75" width="53.25" height="15.75" align-x="43.5" align-y="1068" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="441" left="6" top="1080.75" width="252" height="15.75" align-x="242.25" align-y="1092" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="619" left="6" top="1108.5" width="829.5" height="33.75" align-x="819.75" align-y="1128" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="623" left="924" top="1116" width="29.25" height="15" align-x="935.25" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dove </text> </region> <region region-id="625" left="996" top="1108.5" width="66" height="38.25" align-x="1014" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="25"/> </region> <region region-id="506" left="6" top="1176" width="462" height="15" align-x="6" align-y="1188" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Quest'ultima condizione, dopo alcune semplificazioni si può riscrivere nella forma: </text> </region> <region region-id="628" left="6" top="1204.5" width="844.5" height="38.25" align-x="834.75" align-y="1224" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="630" left="6" top="1266" width="208.5" height="15" align-x="10.5" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> In tutti i termini compare il rapporto: </text> </region> <region region-id="631" left="264" top="1254" width="70.5" height="42.75" align-x="279" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="27"/> </region> <region region-id="633" left="384" top="1266" width="517.5" height="15" align-x="384" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> che fornisce il rapporto tra la massa concentrata e la massa totale della trave: pertanto si ha: </text> </region> <region region-id="639" left="6" top="1320.75" width="571.5" height="15.75" align-x="561.75" align-y="1332" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="661" left="6" top="1350" width="40.5" height="15" align-x="6" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> ovvero: </text> </region> <region region-id="514" left="6" top="1374.75" width="237" height="20.25" align-x="227.25" align-y="1386" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="29"/> </region> <region region-id="513" left="6" top="1422" width="86.25" height="15" align-x="17.25" align-y="1434" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dove si è posto: </text> </region> <region region-id="640" left="6" top="1458.75" width="150" height="20.25" align-x="45.75" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="641" left="6" top="1494.75" width="149.25" height="20.25" align-x="45" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="642" left="6" top="1530.75" width="163.5" height="20.25" align-x="47.25" align-y="1542" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="643" left="6" top="1566.75" width="162.75" height="20.25" align-x="46.5" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="328" left="6" top="1620" width="476.25" height="15" align-x="6" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Le quattro condizioni al contorno si possono scrivere in forma matriciale, come segue </text> </region> <region region-id="329" left="6" top="1649.25" width="98.25" height="78.75" align-x="72" align-y="1692" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:matrix> </ml:apply> <ml:matrix rows="4" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="56" left="6" top="1737" width="243" height="83.25" align-x="44.25" align-y="1782" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="604" left="6" top="1842" width="359.25" height="15" align-x="6" align-y="1854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Conviene procedere per via numerica, senza sviluppi simbolici... </text> </region> <region region-id="541" left="6" top="1884" width="57.75" height="15" align-x="6" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Lunghezza </text> </region> <region region-id="542" left="6" top="1902.75" width="38.25" height="15.75" align-x="18.75" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">l</ml:id> <ml:real>0.8</ml:real> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="543" left="6" top="1950" width="213" height="15" align-x="21" align-y="1962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Materiale: acciaio </text> </region> <region region-id="544" left="6" top="1980.75" width="51.75" height="15.75" align-x="23.25" align-y="1992" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ρ</ml:id> <ml:real>7800</ml:real> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="6"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="37"/> </region> <region region-id="545" left="6" top="2011.5" width="164.25" height="21" align-x="24" align-y="2028" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>206000</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>6</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>206000000000</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="546" left="6" top="2058" width="272.25" height="15" align-x="6" align-y="2070" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sezione circolare di diametro d: </text> </region> <region region-id="547" left="6" top="2083.5" width="117.75" height="21" align-x="21.75" align-y="2100" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">d</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>25</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.025</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="548" left="6" top="2117.25" width="142.5" height="39" align-x="22.5" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">J</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">d</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:real>64</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.9174759848570524E-08</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="549" left="6" top="2159.25" width="158.25" height="39" align-x="38.25" align-y="2184" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="sez">A</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>4</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.00049087385212340522</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="556" left="6" top="2232" width="284.25" height="15" align-x="6" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Massa concentrata </text> </region> <region region-id="645" left="6" top="2262.75" width="47.25" height="20.25" align-x="30.75" align-y="2274" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:real>15</ml:real> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="646" left="6" top="2298.75" width="147" height="20.25" align-x="49.5" align-y="2310" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="trave">m</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.0630528372500487</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="677" left="6" top="2328" width="123" height="42.75" align-x="22.5" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">λ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>4.8970751720583179</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="678" left="192" top="2330.25" width="128.25" height="40.5" align-x="206.25" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>32.11931881322581</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="656" left="6" top="2478.75" width="150" height="20.25" align-x="45.75" align-y="2490" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="657" left="6" top="2514.75" width="149.25" height="20.25" align-x="45" align-y="2526" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="658" left="6" top="2550.75" width="163.5" height="20.25" align-x="47.25" align-y="2562" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="659" left="6" top="2586.75" width="162.75" height="20.25" align-x="46.5" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="660" left="6" top="2631" width="243" height="83.25" align-x="44.25" align-y="2676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="584" left="6" top="2748" width="378.75" height="15" align-x="32.25" align-y="2760" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Cerchiamo le soluzioni dell'equazione caratteristica per via grafica: </text> </region> <region region-id="530" left="6" top="2784" width="92.25" height="16.5" align-x="48" align-y="2796" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">det</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:determinant/> <ml:apply> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="73" left="6" top="2820.75" width="75.75" height="15.75" align-x="22.5" align-y="2832" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:real>0.01</ml:real> </ml:sequence> <ml:real>4</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="263" left="6" top="2856" width="531.75" height="334.5" align-x="6" align-y="2856" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="53"/> <rendering item-idref="54"/> </region> <region region-id="467" left="654" top="2952.75" width="33" height="15.75" align-x="670.5" align-y="2964" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="466" left="654" top="2982.75" width="172.5" height="20.25" align-x="676.5" align-y="2994" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">α</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">det</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.87435002874587253</ml:real> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="56"/> </region> <region region-id="465" left="654" top="3048.75" width="42" height="15.75" align-x="670.5" align-y="3060" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>4.6</ml:real> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="464" left="654" top="3078.75" width="178.5" height="20.25" align-x="676.5" align-y="3090" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">α</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">det</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.950457091893103</ml:real> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="58"/> </region> <region region-id="446" left="6" top="3246.75" width="90.75" height="15.75" align-x="22.5" align-y="3258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:range> <ml:sequence> <ml:real>6</ml:real> <ml:real>6.01</ml:real> </ml:sequence> <ml:real>10.3</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="447" left="6" top="3282" width="552" height="337.5" align-x="6" align-y="3282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="60"/> <rendering item-idref="61"/> </region> <region region-id="463" left="654" top="3366.75" width="48" height="15.75" align-x="670.5" align-y="3378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>7.85</ml:real> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="462" left="654" top="3396.75" width="178.5" height="20.25" align-x="676.5" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">α</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">det</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>7.08282611232247</ml:real> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="63"/> </region> <region region-id="461" left="654" top="3450.75" width="39" height="15.75" align-x="670.5" align-y="3462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>11</ml:real> </ml:define> </math> <rendering item-idref="64"/> </region> <region region-id="460" left="654" top="3480.75" width="184.5" height="20.25" align-x="676.5" align-y="3492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="4">α</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">det</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>10.220066284556294</ml:real> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="65"/> </region> <region region-id="93" left="6" top="3648.75" width="41.25" height="15.75" align-x="21" align-y="3660" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve">α</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="66"/> </region> <region region-id="95" left="84" top="3640.5" width="36.75" height="33.75" align-x="100.5" align-y="3660" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve">β</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="67"/> </region> <region region-id="345" left="6" top="3680.25" width="121.5" height="96.75" align-x="43.5" align-y="3732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="1">α</ml:id> <ml:id xml:space="preserve" subscript="2">α</ml:id> <ml:id xml:space="preserve" subscript="3">α</ml:id> <ml:id xml:space="preserve" subscript="4">α</ml:id> </ml:matrix> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>0.87435002874587253</ml:real> <ml:real>3.950457091893103</ml:real> <ml:real>7.08282611232247</ml:real> <ml:real>10.220066284556294</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="68"/> </region> <region region-id="351" left="246" top="3680.25" width="183.75" height="96.75" align-x="285.75" align-y="3732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="1">β</ml:id> <ml:id xml:space="preserve" subscript="2">β</ml:id> <ml:id xml:space="preserve" subscript="3">β</ml:id> <ml:id xml:space="preserve" subscript="4">β</ml:id> </ml:matrix> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="1">α</ml:id> <ml:id xml:space="preserve" subscript="2">α</ml:id> <ml:id xml:space="preserve" subscript="3">α</ml:id> <ml:id xml:space="preserve" subscript="4">α</ml:id> </ml:matrix> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>1.0929375359323408</ml:real> <ml:real>4.9380713648663788</ml:real> <ml:real>8.8535326404030883</ml:real> <ml:real>12.775082855695368</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="69"/> </region> <region region-id="103" left="6" top="3805.5" width="48.75" height="21" align-x="21.75" align-y="3822" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve">ω</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="70"/> </region> <region region-id="122" left="6" top="3847.5" width="129" height="25.5" align-x="29.25" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:id xml:space="preserve" subscript="1">β</ml:id> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>38.366926447201777</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="350" left="246" top="3840" width="103.5" height="38.25" align-x="267" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">f</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>6.106285995315333</ml:real> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="6"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="72"/> </region> <region region-id="116" left="6" top="3895.5" width="135" height="25.5" align-x="29.25" align-y="3912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:id xml:space="preserve" subscript="2">β</ml:id> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>783.215097168827</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="349" left="246" top="3888" width="115.5" height="38.25" align-x="267" align-y="3912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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width="399" height="15.75" align-x="282" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y'</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="6"/> </region> <region region-id="304" left="6" top="315.75" width="94.5" height="44.25" align-x="42.75" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Y''</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="494" left="192" top="331.5" width="404.25" height="21" align-x="282" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y''</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve" font="1">collect</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="8"/> </region> <region region-id="484" left="6" top="369.75" width="96.75" height="44.25" align-x="45" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Y'''</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>3</ml:real> </ml:degree> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="495" left="192" top="385.5" width="406.5" height="21" align-x="284.25" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y'''</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve" font="1">collect</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="10"/> </region> <region region-id="486" left="6" top="429.75" width="115.5" height="44.25" align-x="39.75" align-y="456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">T</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>3</ml:real> </ml:degree> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="666" left="198" top="444" width="88.5" height="15" align-x="198" align-y="456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Azione di taglio </text> </region> <region region-id="608" left="6" top="499.5" width="150.75" height="25.5" align-x="63.75" align-y="516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="inerz">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="1">M</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="671" left="198" top="504" width="84.75" height="15" align-x="198" align-y="516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Forza d'inerzia </text> </region> <region region-id="306" left="6" top="552" width="138.75" height="15" align-x="6" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Times New Roman" charset="0" size="14"> Condizioni al contorno: </f> </text> </region> <region region-id="12" left="6" top="582" width="69" height="15" align-x="9.75" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Times New Roman" charset="0" size="14"> in x = 0 </f> </text> </region> <region region-id="18" left="6" top="612.75" width="73.5" height="15.75" align-x="38.25" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:symResult> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="13"/> </region> <region region-id="21" left="6" top="648.75" width="151.5" height="15.75" align-x="95.25" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y'</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="14"/> </region> <region region-id="26" left="6" top="702" width="71.25" height="15" align-x="9.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Times New Roman" charset="0" size="14"> in x = l </f> </text> </region> <region region-id="430" left="6" top="727.5" width="391.5" height="21" align-x="95.25" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">Y''</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="15"/> </region> <region region-id="673" left="6" top="763.5" width="1122" height="25.5" align-x="194.25" align-y="780" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="inerz">F</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">collect</ml:id> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:sequence> </ml:command> <ml:symResult> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="16"/> </region> <region region-id="316" left="6" top="816" width="398.25" height="15" align-x="29.25" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Riassunto delle condizioni al contorno (che formano un sistema lineare) </text> </region> <region region-id="42" left="6" top="852.75" width="54" height="15.75" align-x="44.25" align-y="864" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="41" left="6" top="876.75" width="53.25" height="15.75" align-x="43.5" align-y="888" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="18"/> </region> <region region-id="436" left="6" top="900.75" width="288" height="15.75" align-x="278.25" align-y="912" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id 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<ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="19"/> </region> <region region-id="612" left="6" top="931.5" width="946.5" height="25.5" align-x="936.75" align-y="948" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">β</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="20"/> </region> <region region-id="674" left="900" top="962.25" width="234" height="18.75" align-x="904.5" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> in questa equazione si può semplificare β<f family="Times New Roman" charset="0" size="14"> <inlineAttr font-weight="normal" underline="false" line-through="false"> <c val="#f00"> 3 </c> </inlineAttr> </f> </text> </region> <region region-id="320" left="6" top="1002" width="250.5" height="15" align-x="6" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Poniamo per semplicità: α = β l e otteniamo: </text> </region> <region region-id="49" left="6" top="1032.75" width="54" height="15.75" align-x="44.25" align-y="1044" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="21"/> </region> <region region-id="50" left="6" top="1056.75" width="53.25" height="15.75" align-x="43.5" align-y="1068" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="441" left="6" top="1080.75" width="252" height="15.75" align-x="242.25" align-y="1092" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="619" left="6" top="1108.5" width="829.5" height="33.75" align-x="819.75" align-y="1128" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> 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xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="623" left="924" top="1116" width="29.25" height="15" align-x="935.25" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dove </text> </region> <region region-id="625" left="996" top="1108.5" width="66" height="38.25" align-x="1014" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">c</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="25"/> </region> <region region-id="506" left="6" top="1176" width="462" height="15" align-x="6" align-y="1188" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Quest'ultima condizione, dopo alcune semplificazioni si può riscrivere nella forma: </text> </region> <region region-id="628" left="6" top="1204.5" width="844.5" height="38.25" align-x="834.75" align-y="1224" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="630" left="6" top="1266" width="208.5" height="15" align-x="10.5" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> In tutti i termini compare il rapporto: </text> </region> <region region-id="631" left="264" top="1254" width="70.5" height="42.75" align-x="279" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="27"/> </region> <region region-id="633" left="384" top="1266" width="517.5" height="15" align-x="384" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> che fornisce il rapporto tra la massa concentrata e la massa totale della trave: pertanto si ha: </text> </region> <region region-id="639" left="6" top="1320.75" width="571.5" height="15.75" align-x="561.75" align-y="1332" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="661" left="6" top="1350" width="40.5" height="15" align-x="6" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> ovvero: </text> </region> <region region-id="514" left="6" top="1374.75" width="237" height="20.25" align-x="227.25" align-y="1386" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="29"/> </region> <region region-id="513" left="6" top="1422" width="86.25" height="15" align-x="17.25" align-y="1434" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dove si è posto: </text> </region> <region region-id="640" left="6" top="1458.75" width="150" height="20.25" align-x="45.75" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="641" left="6" top="1494.75" width="149.25" height="20.25" align-x="45" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="642" left="6" top="1530.75" width="163.5" height="20.25" align-x="47.25" align-y="1542" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="643" left="6" top="1566.75" width="162.75" height="20.25" align-x="46.5" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="328" left="6" top="1620" width="476.25" height="15" align-x="6" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Le quattro condizioni al contorno si possono scrivere in forma matriciale, come segue </text> </region> <region region-id="329" left="6" top="1649.25" width="98.25" height="78.75" align-x="72" align-y="1692" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">C</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:matrix> </ml:apply> <ml:matrix rows="4" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="56" left="6" top="1737" width="243" height="83.25" align-x="44.25" align-y="1782" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="La variabile è indefinita." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="604" left="6" top="1842" width="359.25" height="15" align-x="6" align-y="1854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Conviene procedere per via numerica, senza sviluppi simbolici... </text> </region> <region region-id="541" left="6" top="1884" width="57.75" height="15" align-x="6" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Lunghezza </text> </region> <region region-id="542" left="6" top="1902.75" width="38.25" height="15.75" align-x="18.75" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">l</ml:id> <ml:real>0.8</ml:real> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="543" left="6" top="1950" width="213" height="15" align-x="21" align-y="1962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Materiale: acciaio </text> </region> <region region-id="544" left="6" top="1980.75" width="51.75" height="15.75" align-x="23.25" align-y="1992" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ρ</ml:id> <ml:real>7800</ml:real> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="6"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="37"/> </region> <region region-id="545" left="6" top="2011.5" width="164.25" height="21" align-x="24" align-y="2028" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>206000</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>6</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>206000000000</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="546" left="6" top="2058" width="272.25" height="15" align-x="6" align-y="2070" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sezione circolare di diametro d: </text> </region> <region region-id="547" left="6" top="2083.5" width="117.75" height="21" align-x="21.75" align-y="2100" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">d</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>25</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-3</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.025</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="548" left="6" top="2117.25" width="142.5" height="39" align-x="22.5" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">J</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">d</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:real>64</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.9174759848570524E-08</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="549" left="6" top="2159.25" width="158.25" height="39" align-x="38.25" align-y="2184" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="sez">A</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>4</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.00049087385212340522</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="556" left="6" top="2232" width="284.25" height="15" align-x="6" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Massa concentrata </text> </region> <region region-id="645" left="6" top="2262.75" width="47.25" height="20.25" align-x="30.75" align-y="2274" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:real>15</ml:real> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="646" left="6" top="2298.75" width="147" height="20.25" align-x="49.5" align-y="2310" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="trave">m</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3.0630528372500487</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="677" left="6" top="2328" width="123" height="42.75" align-x="22.5" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">λ</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="1">M</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>4.8970751720583179</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="678" left="192" top="2330.25" width="128.25" height="40.5" align-x="206.25" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ρ</ml:id> <ml:id xml:space="preserve" subscript="sez">A</ml:id> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>32.11931881322581</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="656" left="6" top="2478.75" width="150" height="20.25" align-x="45.75" align-y="2490" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="657" left="6" top="2514.75" width="149.25" height="20.25" align-x="45" align-y="2526" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="658" left="6" top="2550.75" width="163.5" height="20.25" align-x="47.25" align-y="2562" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="659" left="6" top="2586.75" width="162.75" height="20.25" align-x="46.5" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="660" left="6" top="2631" width="243" height="83.25" align-x="44.25" align-y="2676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="A">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="B">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="C">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="D">f</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="584" left="6" top="2748" width="378.75" height="15" align-x="32.25" align-y="2760" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Cerchiamo le soluzioni dell'equazione caratteristica per via grafica: </text> </region> <region region-id="530" left="6" top="2784" width="92.25" height="16.5" align-x="48" align-y="2796" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">det</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:determinant/> <ml:apply> <ml:id xml:space="preserve" font="17">Δ</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="73" left="6" top="2820.75" width="75.75" height="15.75" align-x="22.5" align-y="2832" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:real>0.01</ml:real> </ml:sequence> <ml:real>4</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="263" left="6" top="2856" width="531.75" height="334.5" align-x="6" align-y="2856" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="53"/> <rendering item-idref="54"/> </region> <region region-id="467" left="654" top="2952.75" width="33" height="15.75" align-x="670.5" align-y="2964" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="466" left="654" top="2982.75" width="172.5" height="20.25" align-x="676.5" align-y="2994" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">α</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">det</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.87435002874587253</ml:real> </result> </ml:eval> </ml:define> <resultFormat numeric-only="true"> <general precision="6" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="56"/> </region> <region region-id="465" left="654" top="3048.75" width="42" height="15.75" align-x="670.5" align-y="3060" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>4.6</ml:real> </ml:define> </math> <rendering 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