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<HTML><HEAD><TITLE>new</TITLE><META content="text/html; charset=gb2312" http-equiv=Content-Type><LINK href="text.css" rel=stylesheet type=text/css><META content="Microsoft FrontPage 4.0" name=GENERATOR></HEAD><body leftmargin="15"><table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">例2 求例1中系统振动的固有频率。</td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic2/30821.34.gif" width="277" height="193"></td> </tr> <tr> <td width="50%">解1：（通过建振动方程求）</td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0" width="290"> <tr> <td width="170">例1已求得标准振动方程</td> <td width="116"><img border="0" src="pic2/30821.35.gif" width="116" height="47"></td> </tr> <tr> <td width="170">则系统振动的固有频率为</td> <td width="116"><img border="0" src="pic2/30821.36.gif" width="115" height="59"></td> </tr> </table> </td> </tr> <tr> <td width="50%">解2：（能量法）</td> </tr> </table> </td> </tr> <tr> <td>设重物自初始上升s，各物体速度如图。系统在任一位置的动能：</td> </tr> <tr> <td><img border="0" src="pic2/30821.37.gif" width="496" height="47"></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>设系统在静平衡位置时，弹簧伸长量为 s0 。令 </td> <td><img border="0" src="pic2/30821.38.gif" width="195" height="28"></td> </tr> </table> </td> </tr> <tr> <td>则：</td> </tr> <tr> <td><img border="0" src="pic2/30821.39.gif" width="184" height="47"></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>而速度振幅：</td> <td><img border="0" src="pic2/30821.40.gif" width="91" height="28"></td> </tr> <tr> <td>则系统振动时最大动能：</td> <td><img border="0" src="pic2/30821.41.gif" width="152" height="47"></td> </tr> </table> </td> </tr> <tr> <td></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">设系统静平衡位置为0势能点，此时弹簧伸长量为s0，系统在任一位置的势能为：</td> <td width="50%" rowspan="2"> <p align="center"><img border="0" src="pic2/30821.42.gif" width="277" height="193"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/30821.43.gif" width="266" height="117"></td> </tr> </table> </td> </tr> <tr> <td><img border="0" src="pic2/30821.44.gif" width="405" height="47"></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">在静平衡位置，给系统虚位移，由虚位移原理：</td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic2/30821.45.gif" width="260" height="197"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/30821.46.gif" width="272" height="27"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/30821.47.gif" width="249" height="27"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/30821.48.gif" width="225" height="27"></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>则系统势能： </td> <td><img border="0" src="pic2/30821.49.gif" width="69" height="44"></td> </tr> <tr> <td>而位移振幅：</td> <td><img border="0" src="pic2/30821.50.gif" width="70" height="28"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>则系统最大势能： </td> <td><img border="0" src="pic2/30821.51.gif" width="89" height="44"></td> </tr> </table> </td> </tr> <tr> <td>系统为单自由度自由振动，由能量法：</td> </tr> <tr> <td> <p align="center"><img border="0" src="pic2/30821.52.gif" width="80" height="25"></td> </tr> <tr> <td>即：</td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic2/30821.53.gif" width="162" height="47"></td> <td> </td> <td><img border="0" src="pic2/30821.54.gif" width="195" height="60"></td> </tr> </table> </td> </tr> <tr> <td> <table border="1" cellpadding="0" cellspacing="0" bordercolor="#008080"> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>注：也可由静力学平衡方程求出关系式： </td> <td><img border="0" src="pic2/30821.55.gif" width="140" height="25"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">在静平衡位置，考虑滚子、滑轮、重物的平衡：</td> <td width="50%" rowspan="8"> <p align="center"><img border="0" src="pic2/30821.56.gif" width="260" height="197"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/30821.57.gif" width="90" height="26"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/30821.58.gif" width="217" height="32"></td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> <tr> <td width="50%"> </td> </tr> </table> </td> </tr> <tr> <td></td> </tr> <tr> <td> <p align="center"> <a href="3082.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a href="3083.htm">↑上一页↑</a> <a href="3084.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr> </table> </BODY></HTML> ⌨️ 快捷键说明
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