Analytical Solutions for Stable and Unstable Period 1 Motions in a Periodically Forced Oscillator With Quadratic Nonlinearity

Abstract

In this note, a closedform solution of periodic motions in a periodically forced oscillator with quadratic nonlinearity is presented without any small parameters. The perturbation method is based on one harmonic term plus perturbation modification, and the traditional harmonic balance is to arbitrarily select harmonic terms with constant coefficients. If harmonic terms are not enough included in the approximate solution, such a solution is not an appropriate, analytical solution for periodic motions, and some analytical solutions cannot be caught.