Abstract
The forced damped parametric driven pendulum oscillators are analyzed numerically via the Galerkin method (GM) and analytically using both ansatz method (AM) and He's frequency formulation. One of the most important features of the obtained numerical approximation using GM is that it can recover a large number of different oscillators related to the problem under study. Moreover, the mentioned equation is solved analytically via both AM and He's frequency formulation. Also, the analytical approximations can recover many different oscillators related to the problem under consideration. Both analytical and numerical approximations are compared with each other and with Runge-Kutta (RK) numerical approximation by estimating both maximum global distance and residual errors. The proposed method can help many authors interested in studying the dynamic problems to explain the mechanics of oscillating to different oscillators in physics, plasma models, engineering, and biological systems.