摘要
通过求解变张力弦振动微分方程的边值问题,给出摆线与摆球的质量比为任意值时单摆系统运动的一般解和本征频率满足的方程.利用该方程求得高精度的单摆系统周期数值解,特别是拟合出单摆系统作基频振动时一个范围大、精度高的周期近似公式.同时将理论与实验进行比较,结果二者相符.
A general solution for the motion of single pendulum system and the equation for its eigenfrequency are given by solving the boundary value problem of equations for vibration of string, in which the tension is variation. The numerical solutions with high accuracy for the period of single pendulum system are obtained using the eigenfrequency equation. A fitting formula for the period of the system being in base-frequency vibration with high precision in the macro-range is found out.
出处
《大学物理》
北大核心
2009年第9期9-12,15,共5页
College Physics
关键词
单摆系统
周期
贝塞尔函数
诺依曼函数
single pendulum system
period
Bessel function
Neumann function
