Parametric excitation for forcing van der Pol oscillator

摘要

The method of time transformation was extended for obtaining the periodic solutions of nonautonomous quasi-linear oscillators governed by second order ordinary differential equations containing a small parametric, and forcing term.The method differs from the time transformation approach in that the independent variable is expanded as a power series in the domain in which the motion is periodic. The extension method was applied to generate the periodic solution, the amplitude, and the period of the solution, several applications of this method, “van der Pol oscillator with forcing term, forcing oscillator with quadratic type damping and van der Pol oscillator with excitation term”, are presented. Analytical results are verified with both numerical method and perturbation method.