Excel在单摆运动分析中的应用

Application of the Excel on Analysis of Pendulum Motions

本文运用求常微方程数值解的四阶龙格-库塔方法,确定了描述单摆运动的非线性微分方程数值解的龙格-库塔公式;用Excel的迭代计算和循环迭代功能确定了数值解,求出单摆在各个时刻的速度和位置;巧用绘制图像和实现动画功能"数"、"形"及"动"连贯形象直观地演示了单摆运动的动态模拟仿真;实现交互性,建立了不同参数情况下研究单摆运动和模拟的平台,得出了单摆无阻尼、有阻尼、摆角为任何角度值时,速度和位置的数值解,速度和位置的曲线和相应的相图;结果显示,Excel在单摆运动分析中的应用,不仅实现数值计算、绘制图像和动画演示,而且弥补实际实验的不足,为物理理论和实验的计算机辅助教学提供了一种简单、直观、高效的方法。

The differential equation of free vibration pendulum movement is described by a second order nonlinear ordinary differential equations. Generally it cannot be solved by analytical methods,the numerical methods are then needed to solve this equation. This paper used Runge-Kutta method which is to find numerical solution of ordinary differential equations to determine the Runge-Kutta formulas of nonlinear differential equations of the pendulum movement. The numerical solution was determined based on iterative computation and cyclic iteration function of Excel,and found the velocity and position of pendulum in each moment. Through drawing image and animation visually it demonstrated the dynamic simulation of pendulum movement by using ＂numeric＂,＂figure＂and ＂move＂coherently.Interactive platform was established to study pendulum movement and simulation in different parameters,numerical solutions and figures of velocity and position and also the phase diagrams can be obtained with damped,undamped and any vibration angle of pendulums. The result showed that the application of Excel on analysis of pendulum can realize the numerical computation,the visual image drawing and animation; meanwhile it has made up the lack of the actual experiment. Computer-aided instruction for theoretical and experimental physics provided simple,intuitive and effective method.