An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator

The nonlinear equations of motion such as the Duffing oscillator equation and its family are seldom addressed in intermediate instruction classical dynamics; this one is problematic because it cannot be solved terms elementary functions before. Thus, work, stability analysis quadratic damping higher-order nonlinearity investigated. Hereinafter, some new analytical solutions to undamped form Weierstrass elliptic function obtained. Posteriorly, a novel exact solution under certain condition (not arbitrary initial conditions) derived detail for first time. Furthermore, obtained camped Runge–Kutta fourth-order (RK4) numerical solution.