问题 计算题

如图所示,两物块M、N的质量分别为,用劲度系数为的足够长的轻弹簧连在一起,放在水平面上,整个系统处于静止状态,现将木块M缓慢下压一端距离后突然释放M,它就上下振动,在振动过程中木块N始终没有离开地面,弹簧的形变量在弹性限度内,求下压距离的最大值。

答案

首先要找出振动的平衡位置,利用振动到的最高点求出振幅,根据简谐运动的规律求出下压最大值。

M静止在平衡位置时,设弹簧的压缩量为

M振动到最高点时,弹簧的伸长量为

振动的振幅为

联立解得:

下压的最大距离等于振幅,得:

完形填空

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多项选择题