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subscript="1begin">θ</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="5029" left="54" top="112.5" width="61.5" height="13.5" align-x="89.25" align-y="122.25" 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:id xml:space="preserve">F1</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">kgf</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5967" left="150" top="112.5" width="65.25" height="13.5" align-x="186" align-y="122.25" 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:id xml:space="preserve">x1'</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m/s</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5968" left="240" top="112.5" width="65.25" height="13.5" align-x="276" align-y="122.25" 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:id xml:space="preserve">y1'</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m/s</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5630" left="54" top="136.5" width="84" height="12" align-x="69" align-y="146.25" 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"> System of equation </text> </region> <region region-id="5032" left="54" top="156.75" width="92.25" height="21" align-x="123.75" align-y="170.25" 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:plus/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="1">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> </region> <region region-id="5033" left="54" top="189" width="195.75" height="33" align-x="99" align-y="206.25" 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:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:apply> <ml:id xml:space="preserve">x1''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="5034" left="54" top="225" width="228" height="33" align-x="131.25" align-y="242.25" 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:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:apply> <ml:id xml:space="preserve">y1''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:id xml:space="preserve">g</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="4140" left="6" top="262.5" width="66.75" height="12" align-x="8.25" align-y="272.25" 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"> 2-nd pendulum </text> </region> <region region-id="5628" left="60" top="286.5" width="232.5" height="12" align-x="70.5" align-y="296.25" 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"> Initial position (x2-y2), force (F2) and velocity (x2'-y2') </text> </region> <region region-id="5099" left="60" top="310.5" width="187.5" height="17.25" align-x="94.5" align-y="320.25" 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:id xml:space="preserve">x2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">L</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve" subscript="1begin">θ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">L</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve" subscript="2begin">θ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="5100" left="60" top="340.5" width="206.25" height="17.25" align-x="94.5" align-y="350.25" 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:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">L</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve" subscript="1begin">θ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">L</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve" subscript="2begin">θ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </math> </region> <region region-id="5641" left="60" top="370.5" width="61.5" height="13.5" align-x="95.25" align-y="380.25" 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:id xml:space="preserve">F2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">kgf</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5971" left="156" top="370.5" width="65.25" height="13.5" align-x="192" align-y="380.25" 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:id xml:space="preserve">x2'</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m/s</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5972" left="258" top="370.5" width="65.25" height="13.5" align-x="294" align-y="380.25" 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:id xml:space="preserve">y2'</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m/s</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5643" left="60" top="394.5" width="84" height="12" align-x="75" align-y="404.25" 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"> System of equation </text> </region> <region region-id="5104" left="60" top="414.75" width="174.75" height="21" align-x="212.25" align-y="428.25" 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:plus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> </region> <region region-id="5105" left="60" top="447" width="135" height="33" align-x="105" align-y="464.25" 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:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:id xml:space="preserve">x2''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="5106" left="60" top="483" width="167.25" height="33" align-x="137.25" align-y="500.25" 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:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:id xml:space="preserve">y2''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:id xml:space="preserve">g</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="4301" left="6" top="514.5" width="38.25" height="12" align-x="23.25" align-y="524.25" 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"> Solution </text> </region> <region region-id="5137" left="66" top="541.5" width="178.5" height="103.5" align-x="97.5" align-y="596.25" 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="6" cols="1"> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">F2</ml:id> </ml:matrix> <ml:apply> <ml:Odesolve method="radau"/> <ml:sequence> <ml:matrix rows="6" cols="1"> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">F2</ml:id> </ml:matrix> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve" subscript="end">t</ml:id> <ml:real>10000</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> </region> <region region-id="5729" left="264" top="611.25" width="84.75" height="32.25" align-x="276.75" align-y="632.25" 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">tt</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="end">t</ml:id> <ml:real>5000</ml:real> </ml:apply> </ml:sequence> <ml:id xml:space="preserve" subscript="end">t</ml:id> </ml:range> </ml:define> </math> </region> <region region-id="5645" left="6" top="670.5" width="105.75" height="12" align-x="15.75" align-y="680.25" 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"> Data for the plot below<sp count="3"/> </text> </region> <region region-id="4525" left="6" top="698.25" width="152.25" height="37.5" align-x="36" align-y="722.25" 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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xml:space="preserve">g</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="dot"/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="dot"/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="5975" left="18" top="895.5" width="143.25" height="36" align-x="46.5" align-y="920.25" 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">ke</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="bl">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="red">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> You can change this value (1-700: manuel or by help Tools/Animation/Record) an see the plot below. </text> </region> <region region-id="6149" left="0" top="252" width="6000" height="6" align-x="0" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="4366" left="24" top="255.75" width="548.25" height="540" align-x="24" align-y="255.75" show-border="false" show-highlight="false" is-protected="true" z-order="-4" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="20"/> <rendering item-idref="21"/> </region> <region region-id="6095" left="144" top="548.25" width="48.75" height="17.25" align-x="162" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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item-idref="25"/> </region> <region region-id="6052" left="432" top="572.25" width="54" height="17.25" align-x="456" align-y="582" 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:id xml:space="preserve" subscript="red">L</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">m</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.2</ml:real> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="6148" left="144" top="590.25" width="40.5" height="17.25" align-x="162" align-y="600" 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" 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is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Initial position (x1-y1), force (F1) and velocity (x1'-y1') </text> </region> <region region-id="5970" left="426" top="68.25" width="85.5" height="189" align-x="426" align-y="68.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="16"/> </region> <region region-id="5027" left="54" top="64.5" width="108.75" height="17.25" align-x="88.5" align-y="74.25" 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:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id 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xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:id xml:space="preserve">g</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="4140" left="6" top="262.5" width="66.75" height="12" align-x="8.25" align-y="272.25" 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"> 2-nd pendulum </text> </region> <region region-id="5628" left="60" top="286.5" width="232.5" height="12" align-x="70.5" align-y="296.25" 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"> Initial position (x2-y2), force (F2) and velocity (x2'-y2') </text> </region> <region region-id="5099" left="60" top="310.5" width="187.5" height="17.25" align-x="94.5" align-y="320.25" 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:id xml:space="preserve">x2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">L</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve" subscript="1begin">θ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">L</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve" subscript="2begin">θ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="5100" left="60" top="340.5" width="206.25" height="17.25" align-x="94.5" align-y="350.25" 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:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">L</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve" subscript="1begin">θ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">L</ml:id> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve" subscript="2begin">θ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </math> </region> <region region-id="5641" left="60" top="370.5" width="61.5" height="13.5" align-x="95.25" align-y="380.25" 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:id xml:space="preserve">F2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">kgf</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5971" left="156" top="370.5" width="65.25" height="13.5" align-x="192" align-y="380.25" 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:id xml:space="preserve">x2'</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m/s</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5972" left="258" top="370.5" width="65.25" height="13.5" align-x="294" align-y="380.25" 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:id xml:space="preserve">y2'</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">m/s</ml:id> </ml:apply> </ml:apply> </math> </region> <region region-id="5643" left="60" top="394.5" width="84" height="12" align-x="75" align-y="404.25" 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"> System of equation </text> </region> <region region-id="5104" left="60" top="414.75" width="174.75" height="21" align-x="212.25" align-y="428.25" 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:plus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> </region> <region region-id="5105" left="60" top="447" width="135" height="33" align-x="105" align-y="464.25" 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:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:id xml:space="preserve">x2''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="5106" left="60" top="483" width="167.25" height="33" align-x="137.25" align-y="500.25" 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:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:id xml:space="preserve">y2''</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:id xml:space="preserve">g</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> </region> <region region-id="4301" left="6" top="514.5" width="38.25" height="12" align-x="23.25" align-y="524.25" 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"> Solution </text> </region> <region region-id="5137" left="66" top="541.5" width="178.5" height="103.5" align-x="97.5" align-y="596.25" 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="6" cols="1"> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">F2</ml:id> </ml:matrix> <ml:apply> <ml:Odesolve method="radau"/> <ml:sequence> <ml:matrix rows="6" cols="1"> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">F2</ml:id> </ml:matrix> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve" subscript="end">t</ml:id> <ml:real>10000</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> </region> <region region-id="5729" left="264" top="611.25" width="84.75" height="32.25" align-x="276.75" align-y="632.25" 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">tt</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="end">t</ml:id> <ml:real>5000</ml:real> </ml:apply> </ml:sequence> <ml:id xml:space="preserve" subscript="end">t</ml:id> </ml:range> </ml:define> </math> </region> <region region-id="5645" left="6" top="670.5" width="105.75" height="12" align-x="15.75" align-y="680.25" 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"> Data for the plot below<sp count="3"/> </text> </region> <region region-id="4525" left="6" top="698.25" width="152.25" height="37.5" align-x="36" align-y="722.25" 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="bl">v</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="4531" left="216" top="698.25" width="158.25" height="37.5" 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</ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="4685" left="6" top="749.25" width="38.25" height="15" align-x="25.5" align-y="758.25" 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="bl">m</ml:id> <ml:id xml:space="preserve" subscript="1">m</ml:id> </ml:define> </math> </region> <region region-id="4686" left="108" top="749.25" width="41.25" height="15" align-x="130.5" align-y="758.25" 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="red">m</ml:id> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:define> </math> </region> <region region-id="4757" left="204" top="749.25" width="35.25" height="15" align-x="222" align-y="758.25" 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="bl">L</ml:id> <ml:id xml:space="preserve" subscript="1">L</ml:id> </ml:define> </math> </region> <region region-id="4758" left="306" top="749.25" width="38.25" height="15" align-x="327" align-y="758.25" 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="red">L</ml:id> <ml:id xml:space="preserve" subscript="2">L</ml:id> </ml:define> </math> </region> <region region-id="4931" left="6" top="777" width="65.25" height="29.25" align-x="37.5" align-y="794.25" 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="bl">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">F1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve">g</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="4932" left="126" top="777" width="71.25" height="29.25" align-x="163.5" align-y="794.25" 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="red">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">F2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve">g</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="5257" left="246" top="785.25" width="81.75" height="15" align-x="255.75" align-y="794.25" 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">t</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="end">t</ml:id> <ml:real>0.0000001</ml:real> </ml:apply> </ml:define> </math> </region> <region region-id="5685" left="12" top="813" width="82.5" height="29.25" align-x="31.5" align-y="830.25" 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="bl">θ</ml:id> <ml:apply> <ml:id xml:space="preserve">atan</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="5690" left="192" top="813" width="122.25" height="29.25" align-x="217.5" align-y="830.25" 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="red">θ</ml:id> <ml:apply> <ml:id xml:space="preserve">atan</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="5974" left="18" top="862.5" width="256.5" height="17.25" align-x="46.5" align-y="872.25" 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">pe</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="dot"/> <ml:id xml:space="preserve">g</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="dot"/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="dot"/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="5975" left="18" top="895.5" width="143.25" height="36" align-x="46.5" align-y="920.25" 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">ke</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="bl">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="red">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> You can change this value (1-700: manuel or by help Tools/Animation/Record) an see the plot below. </text> </region> <region region-id="6149" left="0" top="252" width="6000" height="6" align-x="0" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="4366" left="24" top="255.75" width="548.25" height="540" align-x="24" align-y="255.75" show-border="false" show-highlight="false" is-protected="true" z-order="-4" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="20"/> <rendering item-idref="21"/> </region> <region region-id="6095" left="144" top="548.25" width="48.75" height="17.25" align-x="162" align-y="558" 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:id xml:space="preserve" subscript="bl">θ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">°</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.959672606446208E-05</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <decimal precision="2" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="22"/> </region> <region region-id="6116" left="210" top="548.25" width="65.25" height="17.25" align-x="234" align-y="558" 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:id xml:space="preserve" subscript="red">θ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">°</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-89.816469342294013</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <decimal precision="2" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="23"/> </region> <region region-id="6042" left="426" top="548.25" width="59.25" height="17.25" align-x="453" align-y="558" 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:id xml:space="preserve" subscript="red">m</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="6147" left="144" top="566.25" width="45.75" height="17.25" align-x="165" align-y="576" 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:id xml:space="preserve" subscript="bl">m</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="6052" left="432" top="572.25" width="54" height="17.25" align-x="456" align-y="582" 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:id xml:space="preserve" subscript="red">L</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">m</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.2</ml:real> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="6148" left="144" top="590.25" width="40.5" height="17.25" align-x="162" align-y="600" 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" 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numeric-only="true"> <decimal precision="3" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="30"/> </region> <region region-id="6172" left="480" top="764.25" width="83.25" height="17.25" align-x="514.5" align-y="774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="red">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">m/s</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.11210466252984101</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <decimal precision="3" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="31"/> </region> <region region-id="6185" left="54" top="776.25" width="87" height="17.25" align-x="90" align-y="786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="red">F</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kgf</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.0029706610768398629</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <decimal precision="3" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="32"/> </region> <region region-id="6173" left="474" top="790.5" width="112.5" height="9.75" align-x="487.5" align-y="798" 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 size="8">Created by Valery Ochkov</f> </text> </region> </regions> <binaryContent> <item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/2yQwW6CQBCGZ1wqSFG89NI1wWfwCXowTQ+NJvoAZItUMRIbSpMe++b0n9k9 GWczw8/s9w/LZkTEyD0yVW1Q88OqPHbu61R+XrvW9TFJPCEn2l673mmLnpFJW20/znXV+9bO 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