?? 3082.htm
字號(hào):
<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"><center><b><br>2 振動(dòng)微分方程的建立</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td>除牛頓第二定律外，可以試用各種動(dòng)力學(xué)方法建立<font color="#FF0000">振動(dòng)微分方程</font>。只是將列出的動(dòng)力學(xué)方程寫成位移坐標(biāo)的導(dǎo)數(shù)形式——<font color="#FF00FF">事實(shí)上是含（角）加速度的動(dòng)力學(xué)方程。</font></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">例1 例5-1在重物下加彈簧，設(shè)初始靜止，彈簧為原長(zhǎng)，彈簧系數(shù)為k。可用多種方法求解</td> <td width="50%" rowspan="2"> <p align="center"><img border="0" src="pic2/3082.h12.gif" width="254" height="192"></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>① 動(dòng)能定理；</td> <td><b><font color="#0000FF">√</font></b></td> </tr> <tr> <td>②機(jī)械能守恒定律；</td> <td><b><font color="#0000FF">√</font></b></td> </tr> <tr> <td>③ 動(dòng)量定理；</td> <td><b><font color="#FF0000">×</font></b></td> </tr> <tr> <td>④ 動(dòng)量矩定理；</td> <td><b><font color="#0000FF">√</font></b></td> </tr> <tr> <td>⑤ 達(dá)朗貝爾原理（動(dòng)靜法）；</td> <td><b><font color="#0000FF">√</font></b></td> </tr> <tr> <td>⑥ 動(dòng)力學(xué)普遍方程；</td> <td><b><font color="#0000FF">√</font></b></td> </tr> <tr> <td>⑦ 拉格朗日方程。</td> <td><b><font color="#0000FF">√</font></b></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td>共6大類方法有效。</td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>解：</b><font color="#800000">（動(dòng)能定理）</font></td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic2/3082.h13.gif" width="277" height="193"></td> </tr> <tr> <td width="50%">設(shè)重物自初始上升s，各物體速度如圖。</td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3082.h14.gif" width="215" height="30"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3082.h15.gif" width="45" height="25"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3082.h16.gif" width="327" height="96"></td> </tr> </table> </td> </tr> <tr> <td><img border="0" src="pic2/3082.h17.gif" width="452" height="48"></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>代入（1）式，整理得 </td> <td><img border="0" src="pic2/3082.h18.gif" width="231" height="47"></td> </tr> </table> </td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>對(duì)t求導(dǎo)，得 </td> <td><img border="0" src="pic2/3082.h19.gif" width="308" height="48"></td> <td>含常數(shù)項(xiàng)，非標(biāo)準(zhǔn)形式</td> </tr> </table> </td> </tr> <tr> <td><img border="0" src="pic2/3082.h20.gif" width="302" height="44"></td> </tr> <tr> <td> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>代入（2）式，整理得標(biāo)準(zhǔn)振動(dòng)方程： </td> <td><img border="0" src="pic2/3082.h21.gif" width="116" height="47"></td> </tr> </table> </td> </tr> <tr> <td></td> </tr> <tr> <td> <p align="center"> <a href="3081.htm"><font color="#FF6666">[ 上一節(jié) ]</font></a> <a href="3083.htm"><font color="#00CC00">[ 下一節(jié) ]</font></a> </td> </tr></table></BODY></HTML> ?? 快捷鍵說(shuō)明
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