大角度单摆运动的周期研究

A Study on the Period of Wide-angled Simple Pendulum Movement

对单摆运动进行了讨论。单摆的周期是物理学中的一个基本问题,通过力学分析,建立了单摆的动力学方程,用机械能守恒定律分析了单摆周期,并给出了精确公式。利用三角函数作为一种近似方法,对单摆的动力学方程进行了简化,给出了大角度条件下单摆运动的周期的近似公式。对近似公式和精确公式进行了对比,最后进行了数值计算,结果表明,所得到的单摆运动周期的近似公式在大多数情况下都与精确公式符合的很好。

Simple pendulum movement is dealed with. Its period is a basic problem in physics. A mechanical analysis leads to the dynamics equation of simple pendulm. Using mechanical energy conservation law, the simple pendulum period is analyzed and its exact formula is given. As an approximate method, with the trigonometric function, the simple pendulum dynamical equation is simplified, and the approximate formula for the period of simple pendulum movement is presented. Comparison is made between approximate formula and exact one, ending with numerical calculation. The result shows that the approximate formula of period of simple pendulum movement coincides well with the exact formula in most cases.