单摆周期的近似公式比较

用级数展开积分法、迭代法以及余弦函数法给出了单摆运动周期的3种近似公式.并与椭圆积分得到的周期严格解进行比较,得出在不同摆角时的相对误差,根据实际问题的不同精度要求,选择恰当的近似公式.

The Approximate Solution of the Period of a Simple Pendulum

Three approximate period formulas of a simple pendulum were given by the series expansion integral method, iterative method and the cosine function method. The approximate period was compared with the strict period from the elliptic integral method. A conclusion that according to the different accuracy requirements of practical problems, appropriate approximate formula could be chosen to obtain the relative error at different swing angles was drawn.