A method for investigating free-running and force behavior of almost sinusoidal oscillators with shifting bias

An approach to the investigation of weakly nonlinear shifting-bias (free-running or driven) oscillators is presented. The mathematical modeling proposed for such systems and the stroboscopic technique devised to filter the differential equations responsible for the dynamics of dc and ac (amplitude and phase) components, constitute the keypoints of the analysis. As a by-product, analytical criteria for ascertaining dynamical stability of the oscillations are also derived in explicit closed form. The examples taken into consideration (a third- and a fourth-order oscillator) show that simplicity of use is among the features of the method.