Analytical Approximant to a Quadratically Damped Forced Cubic-Quintic Duffing Oscillator

Abstract

The cubic-quintic Duffing oscillator of a system with strong quadratic damping and forcing is considered. We give elementary approximate analytical solution to this oscillator in terms of exponential and trigonometric functions. We compare the analytical approximant with the Runge–Kutta numerical solution. The approximant allows us to estimate the points at which the solution crosses the horizontal axis.