复摆实验修正阻力影响的研究

Study on the Non-linear Vibration of a Compound Pendulum Affected by Resistance

为了研究复摆实验中空气阻力和刀口处的摩擦力对实验结果的影响,设两者构成的总阻力与速度成正比,比例系数称为阻力系数。依据转动定律,得到在该阻力作用下复摆运动的微分方程。首先对角振幅小于5°时的小角振动情况精确求解,得出有阻力时小角振动周期随阻力系数变化的定量关系,然后采用KBM平均法给出大角振动的近似解析解,得到周期随初始角振幅和阻力系数变化的规律。求解中发现,无论是小角还是大角振动,角振幅随阻力系数的衰减规律完全相同,据此提出通过角振幅衰减的测量,计算出复摆理想(无阻力)振动的周期,修正了阻力对实验结果的影响。

The differential equation of a compound pendulum motion which is affected by resistance was solved.The exact solution of small angle vibration and the approximate analytic so lution of large angle vibration using KBM averaging method were obtained.The relationship of the period varying with the angle amplitude and damping coefficient was given.The strategy to amend the resistance impact in compound pendulum experiment was proposed.