Solution of the damped cubic–quintic Duffing oscillator by using Jacobi elliptic functions

In this paper, we derive an analytical solution of the damped cubic–quintic Duffing oscillator which is based on a rational elliptic form used to obtain exact and approximate solutions of undamped oscillators. We examine different set of system parameter values to assess the accuracy of our derived solution. It is shown that theoretical predictions compares well with the numerical integration solutions obtained by a fourth order Runge–Kutta method. This demonstrates the applicability of rational elliptic forms to solve damped oscillators with higher nonlinear terms.