Analytical Approximant to a Quadratically Damped Duffing Oscillator

The Duffing oscillator of a system with strong quadratic damping is considered. We give an 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. We also solve the oscillator by menas of He’s homotopy method and the famous Krylov–Bogoliubov–Mitropolsky method. The approximant allows estimating the points at which the solution crosses the horizontal axis.