用Matlab模拟x^(2k+1)(k=0,1,2,…)型振荡器与可视化

Simulation and visualization of x^(2k+1)(k=0,1,2,…) oscillator with Matlab

导出了x2k+1(k=0,1,2,…)型振荡器的运动方程。利用Matlab语言和龙格-库塔方法对x2k+1(k=0,1,2,…)型振荡器进行数值模拟并将结果可视化,给出了具体Matlab计算程序和图形用户界面(GUI)。用户通过改变相关参数即可快速得到结果。该程序在Matlab 6.1版本下开发并测试。通过具体实例分别给出了-cx、-cx3-、cx5三种类型振荡器的时间-位移曲线和速度-位移曲线。该系统可用于工科大学物理有关振动的计算机辅助教学。

Equation governing x^（2k＋1）（k=0,1,2,…） oscillators is derived in this paper. The characteristics of x^（2k＋1） （k=0,1,2,…） oscillators is simulated and visualized using Runge-Kutter method with Matlab, Matlab code and a graphical user interface（GUI） are presented. User can quickly obtain results by change of related parameters. This program was developed and tested under Mat.lab version 6.1. For example, the curves of time-displacement and velocity- displacement for -cx, -cx3 and -cx5 oscillators are given respectively. This system may be used as computer aided teaching in vibration for college physics.