New analytic solution of second-order oscillator using multi-time variables technique

In this paper, a new analysis of sinusoidal oscillator amplitude controlled by forced response using the second order differential equation (ODE) is proposed. In general, the amplitude of the complete response is derived where forced response slope is normally assumed to be zero. The value of forced response only at initial time is thus employed to determine the amplitude. But if forced input is dynamic signal the amplitude of complete response gained by using such assumption is different from the experimental result. Thus, a new analysis of amplitude for a dynamic forced response is proposed in this paper. It is found that the forced response at any arbitrary time (not only at the initial time) is presented in a term of natural response magnitude of natural response is therefore directly controlled by forced response. To confirm the theoretical analysis, experimental results have been demonstrated and agreed well with the analysis results.