The modified Lindstedt–Poincare method for solving quadratic nonlinear oscillators

Recently, an analytical solution of a quadratic nonlinear oscillator has been presented based on the harmonic balance method. By introducing a small parameter, a set of nonlinear algebraic equations have been solved which usually appear among unknown coefficients of several harmonic terms. But the method is not suitable for all quadratic oscillators. Earlier, introducing a small parameter to the frequency series, Cheung et al. modified the Lindstedt–Poincare method and used it to solve strong nonlinear oscillators including a quadratic oscillator. But due to some limitations of both parameters, a changed form of frequency-related parameter (introduced by Cheung et al.) has been presented for solving various quadratic oscillators.