An Application of Laplace Transform, Inverse Laplace Transform and Pade’s Approximant in the Periodic Solution of Duffing Equation of Motion

The main objective of this research is to obtain the periodic solution by inserting the ideas of Laplace Transformation, Pade's Approximant and Inverse Laplace Transformation are applied.In this research article the Standard Duffing Equation of motion possessing symmetric oscillations is examined by using the Sumudu Transform Series Decomposition Method.The Duffing oscillator is a periodically forced oscillator with a nonlinear elasticity.For this type of oscillatory system there are frequencies at which the vibration suddenly jumps and these jumps depend upon whether the frequency is increasing or decreasing.Between these frequencies, multiple solutions exist for a given frequency of excitation, and the initial conditions determine which of these solutions represents the response of the system.The Sumudu Transform Series Decomposition Method (STSDM) is claimed as an efficient method for solving problems in Engineering and Science fields.It gives divergent series solution.This article explores on studying the application capacity of STSDM in getting solution for symmetric oscillations of Duffing Equation of Motion which are simple and nonlinear.