延边大学《大学物理》课件 第九章 振动

物体或物体的某一部分在一定位置附近来回往复的运动

实例:心脏的跳动，钟摆，乐器，地震等1机械振动平衡位置一简谐运动E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

旋转矢量自Ox轴的原点O作一矢量，使它的模等于振动的振幅A，并使矢量在Oxy平面内绕点O作逆时针方向的匀角速转动，其角速度与振动频率相等，这个矢量就叫做旋转矢量.E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

以

为原点旋转矢量的端点在轴上的投影点的运动为简谐运动.E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

以

为原点旋转矢量的端点在轴上的投影点的运动为简谐运动.E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410用旋转矢量图画简谐运动的

图E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410讨论

相位差：表示两个相位之差（1）对同一简谐运动，相位差可以给出两运动状态间变化所需的时间．E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410（2）对于两个同频率的简谐运动，相位差表示它们间步调上的差异（解决振动合成问题）.E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410同步为其它超前落后反相E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

例一质量为0.01kg的物体作简谐运动，其振幅为0.08m，周期为4s，起始时刻物体在x=0.04m处，向ox轴负方向运动（如图）.试求（1）t=1.0s时，物体所处的位置和所受的力；

E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410代入解已知求（1）E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410代入上式得可求（1）E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410（2）由起始位置运动到x=-0.04m处所需要的最短时间.法一设由起始位置运动到x=-0.04m处所需要的最短时间为tE6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410法二起始时刻时刻E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F654109-1简谐运动振幅周期和频率相位9-2旋转矢量9-3单摆和复摆9-4简谐运动的能量本章目录选择进入下一节：9-5简谐运动的合成9-6阻尼振动受迫振动共振ENDE6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

简谐运动最简单、最基本的振动谐振子作简谐运动的物体简谐运动复杂振动合成分解2简谐振动E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

弹簧振子的振动E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410振动的成因：回复力+惯性E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410令3弹簧振子的运动分析得即简谐运动的特征：加速度与位移的大小x成正比，方向相反E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410简谐运动的微分方程积分常数，根据初始条件确定解方程设初始条件为:解得简谐运动方程E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410由得其中简谐运动方程E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410图图图取E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410简谐运动方程二振幅图E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410三周期、频率弹簧振子周期

周期注意图E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

频率圆频率周期和频率仅与振动系统本身的物理性质有关图E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410频率为例如，心脏的跳动80次/分周期为大象0.4~0.5马0.7~0.8猪1~1.3兔1.7松鼠6.3鲸0.13动物的心跳频率(参考值,单位:Hz)

E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E57FAB79DBF2DB6715F2B3FB877C24F65410

昆虫翅膀振动的频率（Hz）

雌性蚊子355~415雄性蚊子455~600苍蝇330

黄蜂220E6636B02012BD195C019CE06C16E3064C63D09E32711A616D0819A1A3DE598FE8F058803BC41BA960B49D5F0472B73A72FC0F2BE2AA53EFE6A07217E5