Nonlinear oscillations with multiple forcing terms (Q1092695)

The problem of determining the transient response of a nonlinear oscillator of the form ü\(+u=\epsilon f(u,\dot u)+E(t)\) is studied by the method of multiple time scales, using the symbolic computation system MACSYMA, when the excitation E(t) consists of a finite number of harmonic forcing terms. Here \(\epsilon\) is a small parameter and f(u,\D{u}) is a nonlinear function of its arguments. In particular, the Van der Pol and Duffing oscillators are studied in detail. It is found that when the forcing frequencies are not close to each other or close to the primary resonance of the system, then the response of the system is analogous to the behavior when only one forcing term is present. However, when the forcing frequencies are close to each other or close to the primary resonance, then the behavior is quite different, exhibiting certain oscillations not observed in the case of one forcing term.