The effect of damping on autoresonant (nonstationary) excitation

When a nonlinear oscillator with an amplitude dependent frequency is driven by a swept frequency drive, the oscillator's amplitude will, in some circumstances, automatically adjust itself so that the oscillator's nonlinear frequency closely matches the drive frequency. This phenomenon is called autoresonance, and allows the amplitude of the oscillator to be controlled simply by sweeping the drive frequency. Previous studies of autoresonance were in undamped systems; the effect of damping on autoresonance is considered here. In particular, the question of a threshold for entering autoresonance in a dissipative system is investigated. The resulting theory accurately describes the behavior of experiments on the diocotron mode in pure-electron plasmas.