题目内容
试证明竖直方向的弹簧振子的振动是简谐运动
如图所示,设振子的平衡位置为O,向下方向为正方向,此时弹簧的形变为
,根据胡克定律及平衡条件有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145345221440.gif)
①
当振子向下偏离平衡位置为
时,回复力(即合外力)为
②
将①代人②得:
,可见,重物振动时的受力符合简谐运动的条件
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534522204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145345221440.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534538484.gif)
当振子向下偏离平衡位置为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534553187.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534569602.gif)
将①代人②得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534585400.gif)
如图所示,设振子的平衡位置为O,向下方向为正方向,此时弹簧的形变为
,根据胡克定律及平衡条件有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145345221440.gif)
①
当振子向下偏离平衡位置为
时,回复力(即合外力)为
②
将①代人②得:
,可见,重物振动时的受力符合简谐运动的条件
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534522204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241145345221440.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534538484.gif)
当振子向下偏离平衡位置为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534553187.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534569602.gif)
将①代人②得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114534585400.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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