Third order oscillators with independently adjustable frequency, amplitude and transient response

A class of third order harmonic oscillators with frequency, amplitude and transient response controlled by three separate sets of parameters is derived. A simplified group of oscillators is described in which there are only three parameters, one which controls the frequency, another the amplitude, and the third the transient response. Each oscillator contains a single nonlinearity, which can be either of the saturation or the dead space type. The mathematical analysis is based on linearizing the nonlinearity by means of the sinusoidal describing function. The transient response is studied by considering small amplitude perturbations away from the oscillator's limit cycle. The results of analogue computer simulations are presented with emphasis on the relationship between transient response and the gain controlling it.