On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications

In this study, a novel analytical solution to the integrable undamping Duffing equation with constant forced term is obtained. Also, new approximate (semianalytical) for nonintegrable linear damping oscillator reported. The given in terms of Weierstrass elliptic function arbitrary initial conditions. With respect it, semianalytical constructed depending on ansatz and exact standard (in absence both terms). A comparison between obtained solutions Runge–Kutta fourth-order (RK4) carried out. Moreover, some complicated equations such as pendulum equation, cubic-quintic Helmholtz–Duffing are reduced oscillator, which its known. As practical application, proposed techniques applied investigate characteristics behavior signal oscillations arising RLC circuit externally voltage.