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list-style-type="inherit" tabs="inherit"> <f family="Times New Roman" charset="0" size="14"> <i>in x = 0</i> </f> </p> </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="12"/> </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" 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margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Times New Roman" charset="0" size="14"> <i>in x = l</i> </f> </p> </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> 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<ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k</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: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:minus/> <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:mult/> <ml:id xml:space="preserve">k</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:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </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">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:mult/> <ml:id xml:space="preserve">k</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:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="15"/> </region> <region region-id="316" left="6" top="852" width="398.25" height="15" align-x="29.25" align-y="864" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Riassunto delle condizioni al contorno (che formano un sistema lineare)</p> </text> </region> <region region-id="42" left="6" top="888.75" width="54" height="15.75" align-x="44.25" align-y="900" 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="16"/> </region> <region region-id="41" left="6" top="912.75" width="53.25" height="15.75" align-x="43.5" align-y="924" 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> 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<ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <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">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:mult/> <ml:id xml:space="preserve">k</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:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k</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: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:minus/> <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:mult/> <ml:id xml:space="preserve">k</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:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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:mult/> <ml:id xml:space="preserve">k</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:real>0</ml:real> </ml:apply> </math> <rendering item-idref="19"/> </region> <region region-id="320" left="6" top="1038" width="250.5" height="15" align-x="6" align-y="1050" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Poniamo per semplicità: α = β l e otteniamo:</p> </text> </region> <region region-id="49" left="6" top="1068.75" width="54" height="15.75" align-x="44.25" align-y="1080" 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="20"/> </region> <region region-id="50" left="6" top="1092.75" width="53.25" height="15.75" align-x="43.5" align-y="1104" 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="21"/> </region> <region region-id="441" left="6" top="1116.75" width="252" height="15.75" align-x="242.25" 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: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="22"/> </region> <region region-id="505" left="6" top="1145.25" width="751.5" height="39" align-x="741.75" align-y="1170" 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:minus/> <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: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:real>3</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:id xml:space="preserve">k</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:parens> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k</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: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: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:real>3</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:parens> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </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">E</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <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:real>3</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:id xml:space="preserve">k</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:parens> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <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: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:real>3</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:id xml:space="preserve">k</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:parens> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="506" left="6" top="1212" width="299.25" height="15" align-x="6" align-y="1224" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Quest'ultima condizione si può riscrivere nella forma:</p> </text> </region> <region region-id="514" left="6" top="1242.75" width="237" height="20.25" align-x="227.25" align-y="1254" 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="24"/> </region> <region region-id="513" left="6" top="1290" width="86.25" height="15" align-x="17.25" align-y="1302" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">dove si è posto:</p> </text> </region> <region region-id="516" left="6" top="1312.5" width="46.5" height="39" align-x="19.5" align-y="1332" 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">h</ml:id> <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:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="25"/> </region> <region region-id="520" left="6" top="1363.5" width="164.25" height="25.5" align-x="45.75" align-y="1380" 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:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:id xml:space="preserve">k</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:define> </math> <rendering item-idref="26"/> </region> <region region-id="521" left="6" top="1399.5" width="170.25" height="25.5" align-x="45" align-y="1416" 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:neg/> <ml:id xml:space="preserve">k</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:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:define> </math> <rendering item-idref="27"/> </region> <region region-id="523" left="6" top="1435.5" width="177.75" height="25.5" align-x="47.25" align-y="1452" 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:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:id xml:space="preserve">k</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:define> </math> <rendering item-idref="28"/> </region> <region region-id="525" left="6" top="1471.5" width="177" height="25.5" align-x="46.5" align-y="1488" 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:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:id xml:space="preserve">k</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:define> </math> <rendering item-idref="29"/> </region> <region region-id="328" left="6" top="1530" width="409.5" height="30" align-x="6" align-y="1542" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Le quattro condizioni al contorno si possono scrivere in forma matriciale, come segue</p> </text> </region> <region region-id="329" left="6" top="1559.25" width="98.25" height="78.75" align-x="72" align-y="1602" 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="30"/> </region> <region region-id="56" left="6" top="1647" width="243" height="83.25" align-x="44.25" align-y="1692" 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="31"/> </region> <region region-id="604" left="6" top="1752" width="359.25" height="15" align-x="6" align-y="1764" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Conviene procedere per via numerica, senza sviluppi simbolici...</p> </text> </region> <region region-id="541" left="6" top="1782" width="57.75" height="15" align-x="6" align-y="1794" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Lunghezza</p> </text> </region> <region region-id="542" left="6" top="1800.75" width="29.25" height="15.75" align-x="18.75" align-y="1812" 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>1</ml:real> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="543" left="6" top="1848" width="213" height="15" align-x="21" align-y="1860" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Materiale: acciaio </p> </text> </region> <region region-id="544" left="6" top="1878.75" width="51.75" height="15.75" align-x="23.25" align-y="1890" 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="33"/> </region> <region region-id="545" left="6" top="1909.5" width="164.25" height="21" align-x="24" align-y="1926" 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="34"/> </region> <region region-id="546" left="6" top="1956" width="272.25" height="15" align-x="6" align-y="1968" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Sezione circolare di diametro d:</p> </text> </region> <region region-id="547" left="6" top="1981.5" width="111.75" height="21" align-x="21.75" align-y="1998" 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>20</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>0.02</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="548" left="6" top="2015.25" width="142.5" height="39" align-x="22.5" align-y="2040" 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>7.8539816339744827E-09</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="549" left="6" top="2057.25" width="158.25" height="39" align-x="38.25" align-y="2082" 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>0.00031415926535897931</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="556" left="6" top="2118" width="125.25" height="15" align-x="6" align-y="2130" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Rigidezza della molla:</p> </text> </region> <region region-id="557" left="6" top="2149.5" width="124.5" height="21" align-x="21.75" align-y="2166" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:real>20000</ml:real> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>20000</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="559" left="6" top="2198.25" width="128.25" height="40.5" align-x="20.25" align-y="2220" 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>25.695455050580644</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="582" left="6" top="2254.5" width="111" height="39" align-x="21" 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">h</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <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:pow/> <ml:id xml:space="preserve">l</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1617.9202165987435</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="40"/> </region> <region region-id="564" left="6" top="2323.5" width="164.25" height="25.5" align-x="45.75" align-y="2340" 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:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:id xml:space="preserve">k</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:define> </math> <rendering item-idref="41"/> </region> <region region-id="565" left="6" top="2359.5" width="170.25" height="25.5" align-x="45" align-y="2376" 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:neg/> <ml:id xml:space="preserve">k</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:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:define> </math> <rendering item-idref="42"/> </region> <region region-id="566" left="6" top="2395.5" width="177.75" height="25.5" align-x="47.25" align-y="2412" 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:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:id xml:space="preserve">k</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:define> </math> <rendering item-idref="43"/> </region> <region region-id="567" left="6" top="2431.5" width="177" height="25.5" align-x="46.5" align-y="2448" 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:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</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:id xml:space="preserve">k</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:define> </math> <rendering item-idref="44"/> </region> <region region-id="580" left="6" top="2469" width="243" height="83.25" align-x="44.25" align-y="2514" 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="45"/> </region> <region region-id="584" left="6" top="2574" width="378.75" height="15" align-x="32.25" align-y="2586" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Cerchiamo le soluzioni dell'equazione caratteristica per via grafica:</p> </text> </region> <region region-id="530" left="6" top="2604" width="92.25" height="16.5" align-x="48" align-y="2616" 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="46"/> </region> <region region-id="73" left="6" top="2628.75" width="84.75" height="15.75" align-x="22.5" align-y="2640" 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>6.2</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="263" left="6" top="2664" width="551.25" height="337.5" align-x="6" align-y="2664" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="48"/> <rendering item-idref="49"/> </region> <region region-id="467" left="654" top="2760.75" width="42" height="15.75" align-x="670.5" align-y="2772" 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>3.5</ml:real> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="466" left="654" top="2790.75" width="178.5" height="20.25" align-x="676.5" align-y="2802" 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>2.7350261563363816</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="51"/> </region> <region region-id="465" left="654" top="2856.75" width="33" height="15.75" align-x="670.5" align-y="2868" 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>7</ml:real> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="464" left="654" top="2886.75" width="178.5" height="20.25" align-x="676.5" align-y="2898" 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>4.8179815569094941</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="53"/> </region> <region region-id="446" left="6" top="3030.75" width="90.75" height="15.75" align-x="22.5" align-y="3042" 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>7</ml:real> <ml:real>7.01</ml:real> </ml:sequence> <ml:real>11.5</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="447" left="6" top="3066" width="559.5" height="337.5" align-x="6" align-y="3066" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="55"/> <rendering item-idref="56"/> </region> <region region-id="463" left="654" top="3150.75" width="39" height="15.75" align-x="670.5" align-y="3162" 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>10</ml:real> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="462" left="654" top="3180.75" width="178.5" height="20.25" align-x="676.5" align-y="3192" 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>7.8806627529328326</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="461" left="654" top="3234.75" width="39" height="15.75" align-x="670.5" align-y="3246" 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>13</ml:real> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="460" left="654" top="3264.75" width="184.5" height="20.25" align-x="676.5" align-y="3276" 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>11.004902304022556</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="60"/> </region> <region region-id="93" left="6" top="3450.75" 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