单摆近似周期的新形式及构造分析  

A new approximate formula and some analyses on constructing for the period of a simple pendulum

作　　者：薛德胜[1] 周钊[1] 高美珍[1] 

机构地区：[1]兰州大学物理科学与技术学院,甘肃兰州730000

出　　处：《大学物理》2010年第8期25-28,共4页College Physics

摘　　要：通过对比单摆严格周期的级数展开式,给出了一个新的单摆周期近似公式及其修正形式.在振幅小于114°(136°)的范围内,近似公式(修正形式)的计算结果相对于严格周期的数值计算结果相对误差小于1‰.同时,对单摆近似周期的构造进行了分析.Comparing with the series expansion of the exact period,a new approximate fornmla and its modulated form for the period of the simple pendulum are presented.The constructed formula and its modulated form can be applied in the amplitudes of 114° and 136°,respectively,its relative error is less than 1‰.Some analyses on constructing of the period of a simple pendulum are discussed.

关 键 词：单摆 周期 近似解 级数展开 

分 类 号：O313.1[理学—一般力学与力学基础]