Lagging motion of forced nonlinear oscillators

The lagging motion of nonlinear oscillators with respect to the externally driven field, which has never been discussed previously, was treated analytically and the calculation results were compared with the observed results. Such lagging motion may occur in nonlinear systems whose behavior crucially depends on the frequency of the applied force. The lagging motion of the nonlinear oscillator with respect to the harmonically driven field made the oscillator respond in a way that reduced the effect of the applied field. The calculation considering the lagging motion yielded proper results in the expansion ratio and trajectories in phase plane for the oscillating bubble under ultrasound and the frequency spectrum for a forced inverted pendulum.