Study on the free vibration of odd power oscillators

摘要

The cycle formula of undamped free vibration of odd power oscillators has been gotten by theoretical analysis. The formula shows that the cycle is related to the initial conditions. The numerical experiments reveal that there are three states such as damped oscillation, critical damped oscillation and overdamped oscillation while an odd power oscillator moves in linear damping force. These situations are same as that of a linear oscillator. Unlike the linear oscillator, the critical damping constant of an odd power oscillator is related to the initial conditions. The quantitative expression of the critical damping constant changing with system parameters and initial conditions has been obtained. By analyzing of numerical experimental data, the exponential decay law of the amplitude of an odd power oscillator which moves in damped state has been discovered.