An approximation technique for solving anti-symmetric constant force and anti-symmetric quadratic nonlinear oscillators

Abstract

Earlier, an approximation technique was presented for solving strong nonlinear oscillator equations. Due to arising algebraic complexities, the method fails to determine suitable solutions of some nonlinear oscillators such as quadratic oscillators, the cubical Duffing oscillator of softening springs, and pendulum equations. Then, rearranging an algebraic equation related to amplitude and frequency, the method covers the noted problems. In this article, the latter technique is applied to handling anti-symmetric constant force oscillators and anti-symmetric quadratic nonlinear oscillators.