Forced oscillations of a damped, Duffing oscillator are explored in this chapter.
For weak nonlinearities and weak damping, a perturbation method is used to obtain
an analytical approximation for the primary resonance response. In order to study
the stability of periodic responses of the forced Duffing oscillator, local stability
analysis is carried out on the equations describing the slow time-scale evolution.
In addition, secondary resonance corresponding to strong (hard) excitation is also
discussed. The combination of analytical and numerical investigations presented in
this chapter is used to illustrate the dramatic jump behaviour and the rich variety
of nonlinear phenomena possible in this system.