Transition through resonance in linear and nonlinear systems

In this work an asymptotic method known as the Krylov- Bogol iubov-Mit ropolsky (KBM) method is used to analyze linear and nonlinear systems. A system of first order equations for amplitude and phase is deduced. Using these first order equations the amplitude-response is approximated. The amplitude-response is then compared with the displacement response obtained by the Runge-Kutta method. Also, a comparative study is made between the stationary and nonstat ionary resonances in linear and nonlinear systems. The effect of linear variation of forcing frequency on the amplitude of the systems is closely examined. The consequence of different sweep rates on the amplitudes of the systems is also discussed