International Journal of Modern Physics and Applications
Articles Information
International Journal of Modern Physics and Applications, Vol.5, No.2, Jun. 2019, Pub. Date: Jun. 15, 2019
Approximate Solution of Single Spring Moving System for Damped and Undamped Simple Harmonic Motion by Using Homotopy Perturbation Method
Pages: 26-37 Views: 146 Downloads: 36
Authors
[01] Mohammad Masud Rana, Department of Mathematics, Faculty of Science, Islamic University, Kushtia, Bangladesh.
[02] Ahammodullah Hasan, Department of Mathematics, Faculty of Science, Islamic University, Kushtia, Bangladesh.
Abstract
In this paper, Homotopy perturbation method (HPM) is applied to find the approximate solution of simple harmonic motion of single spring equation, which is known a well-known nonlinear ordinary differential equation. The Homotopy Perturbation Method deforms a difficult problem into a simple problem which can be easily solved. Firstly, the approximate solution of single spring equation is developed using initial conditions. Then the results are compared with the results obtained by Numerical solutions. Finally, Homotopy Perturbation Method (HPM) is applied to find the approximate solution of single spring equation with initial conditions. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. Some examples are presented to show the ability of the method for moving single spring equation.
Keywords
Homotopy Perturbation Method (HPM), Simple Harmonic Motion, Nonlinear Differential Equation, Damped, Undamped, Approximate Solution, Numerical Solution
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