Published Paper Details:

The generic version of the Duffing equation is examined in this article. This problem can be solved with beginning conditions using an adaptation of the power series approach. The power series method's convergence theorem is demonstrated. The Duffing equation is a nonlinear second-order differential equation that models the behavior of a driven, damped oscillator with cubic nonlinearity. In this study, we apply the power series method to obtain an approximate solution to the Duffing equation. The power series expansion expresses the displacement x(t) as an infinite sum of powers of time, which is substituted into the equation to generate a system of recursive equations for the coefficients of the series. By solving these equations iteratively, we determine the approximate solution for small driving force, weak nonlinearity, or for short times. The method provides an effective way to analyze the system's behavior under small perturbations and serves as a foundation for exploring more complex nonlinear oscillatory systems. The approach is validated through the calculation of the first few terms in the series expansion, providing insight into the dynamics of the oscillator for various values of the system parameters such as damping, linear stiffness, and nonlinear stiffness.