任意摆角单摆运动周期的一个近似公式

利用线性插值的方法，提出了在一个任意摆角条件下的单摆运动周期的近似公式.同时利用Mathematica软件，对在不同摆角下的单摆振动周期进行了精确计算，并绘制出了精确解的曲线.将推导出的近似公式与该精确解及其他近似公式进行了对比.结果表明：该近似公式的推导为解决类似问题提供了一个较好的思路，其结果与精确解也符合得很好.而且，从推导过程得出的图像中可比较直观地看出单摆作简谐振动所需的小角度条件.

Approximate period formula of simple pendulum for any amplitude

By using the method of linear interpolation,an approximate period formula of a simple pendulum is derived.Meanwhile,by using Mathematica,the accurate results of the period at different amplitude are calculated and the subsequent curve based on these data is plotted.The results show that the derivation gives a good thinking way for the solution of such problems.By the comparison with the accurate formula and other formulae,this formula proves to be fairly precise.Besides,the necessary requirement of a little amplitude for a harmonic vibration of a simple pendulum can be seen clearly from the course of derivation.