线性阻尼对李萨如图形的影响

Lissajous' figure of the damping harmonic oscillator

在理论分析的基础上,利用Mathematica软件数值研究了线性阻尼对作为二维简谐振子运动轨迹的李萨如图形的影响。发现阻尼的作用一方面使分振动的振幅以指数方式减小,减小的时间常数与阻尼的大小成反比,结果图形迅速向原点收缩;另一方面使分振动的频率减小,结果图形发生缓慢地变形。

On the basis of theoretical analysis, the Lissajous＇figure of a 2-dimentional damping harmonic oscillator is studied numerically using the Mathematica. We find that the amplitude of damping oscillator decreases exponentially, and the time constant is inversely proportional to the damping coefficient, on the other hand the frequency of the vibration also decreases so that the figure is deformation slowly.