Abstract
The present study suggests a very simple, effective new method to study the damping quadratic–cubic nonlinear oscillation in physical phenomena such as fluid, solid-state physics, optics, plasma physics, dispersion, and convection systems with no perturbation. The damping nonlinear oscillation is converted to its equivalent linear oscillation. The exact solution of the corresponding linear oscillation is verified by the first-order homotopy perturbation method which shows an exact agreement. Stability conditions are imposed from the frequency formula. The accuracy of the proposed approach has shown that the approximate analytical solutions are in excellent agreement with the corresponding exact solutions.
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