利用机械能守恒求解非惯性系单摆的振动周期

SOLUTION OF VIBRATION PERIOD OF SIMPLE PENDULUM IN NON-INERTIAL SYSTEM BY CONSERVATION OF MECHANICAL ENERGY

由于不同的非惯性系具有不同的加速度,导致单摆在不同的非惯性系中具有不同的振动周期,所以有必要掌握非惯性系下单摆振动周期的计算.基本的计算方法是利用非惯性系动力学方程,结合受力分析求解,但这种方法既要考虑惯性力,又需要进行力的分解,比较麻烦.本文通过引入惯性力势能,给出非惯性系机械能守恒定律,并利用机械能守恒定律对处于特定非惯性系中的单摆周期进行分析计算,得出非惯性系中单摆的振动周期不仅与单摆自身属性有关,而且与非惯性系的运动加速度或角速度有关的结论.

Due to different accelerations in different non-inertial systems, vibration periods of the simple pendulum are different in these different non-inertial systems. So it is necessary to grasp calculation of the simple pendulum cycle in non-inertial system. The most basic method is to use the dynamical equation of inertial system combined with the force analysis. But this method is troublesome, because the inertia force must be considered and the decomposition of forces are needed. In this paper, by introducing inertia force potential energy, the law of conservation of mechanical energy in non-inertial system is given, and the simple pendulum cycle is calculated in specific non-inertial system. It is concluded that the vibration period of simple pendulum in non-inertial system is not only related with the own properties of pendulum, but also related to the acceleration or the angular velocity of the non-inertial system.