摆球质量减少导致周期变化问题的探讨

Discussion on the Changed Cycle of Simple Pendulum Spheroid Caused by Its Quality Reduction

根据谐振动理论,分别用微积分推导和实验测定的方法,分析了一类常见的关于摆球质量减少的单摆周期问题,得到周期T随液面位置h(质量)变化的函数关系式,以及周期T随液面h变化的曲线,较精确和直观地展示了因摆球质量减少而导致周期变化的规律。并将此类问题的讨论扩展,分析了球壳质量对壳内水(装满)的质量比例系数K的大小对周期变化幅度和规律的影响。

According to the theory of harmonic motion,the cycle of the simple pendulum is analyzed by infinitesimal and experiment respectively,the formulation and the function curve of the cycle T altered with the location of the liquid surface(mass) are obtained,the law of pendulum cycle changed with the pendulum ball's mass reduced is showed more accurately and obviously.As extension,the affection on the range and orderliness of the cycle is analyzed about the ratio K between the spherical shell's mass and the water's mass when the shell is full.