慢变振幅法在研究单摆运动中的应用

The Applications of the Slow Swing Method to the Simple Pendulum

为了研究实际单摆系统的运动规律,考虑了单摆振动过程受到的粘滞性阻尼力,由慢变振幅法给出了实际单摆系统微分方程的近似解.慢变振幅法近似解的计算结果与微分方程的直接数值解一致.结果表明,实际单摆系统的振幅随时间按指数规律衰减;振动的周期随初始振幅的增大而增大,随振动时间的延长而减小.用慢变振幅法给出的系统近似解能准确的描述实际单摆系统的运动规律.

For discussing the vibration disciplinarian of the simple pendulum, the approximate solution of the vibration differential equation was given regarding the sticky resistance. The approximate solution was accord with the numerical solution of the differential equation. The result shows the swing has the character of exponent attenuation with time,and the period increases with the increase of the swing and was shorter with the vibration continuance. The approximately solution of the slow swing method well and truly describes the vibration rule.