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本文首先推导质点做简谐运动的周期的一般公式,对偏角很小时单摆的振动进一步理想化,假设摆球在通过平衡位置的水平直线上往复运动.根据简化的单摆模型求出:(1)做固有振动的单摆;(2)匀加速上升(或下降)的电梯中的单摆;(3)在匀强电场或匀强磁场中的单摆的回复力比例系数,再由简谐运动的周期公式求出这几种单摆的周期,不需要引入等效重力加速度和等效摆长的概念.
In this paper, the general formula of the period of simple harmonic motion is deduced firstly. The vibration of the pendulum is further idealized when the declination angle is small, and the reciprocating motion of the pendulum is assumed on the horizontal straight line passing through the equilibrium position. According to the simplified pendulum model, (1) a single pendulum which is an inherent vibration; (2) a pendulum in an elevator which accelerates (or descends) uniformly; (3) a coefficient of restitution force of a pendulum in a uniform electric field or a uniform magnetic field, Simple harmonic motion cycle formula to find these types of pendulum cycle, do not need to introduce the concept of equivalent gravitational acceleration and equivalent swing length.