Waluya, S. B. (2015) METODE AVERAGING UNTUK MENYELESAIKAN PERSAMAAN DIFERENSIAL NONLINEAR PENDULUM ELASTIS. UNNES Journal of Mathematics, 4 (1). pp. 21-28. ISSN 2252-6943

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Abstract

In this study, the oscillation of the two-dimensional elastic pendulum is investigated to get the equations of motion. Elastic pendulum can move like a spring that hung vertically and also like a simple pendulum . At the beginning of the motion, assumed a spring-like motion (vertical oscillation) dominates pendulum-like behavior (horizontal oscillation). Based on this lead to the solution of equation of motion in the form simple harmonic motion for the vertical component and for the horizontal component, obtained nonlinear differential equation similar with the Mathieu equation. In this study, the Mathieu equation will be the main concern. The equation will be solved by one of the perturbation technique, that is averaging method to obtain the approximation solution. The advantages of using this method are simple and the stages of processing to solve differential equation is short. To chek the accuracy of averaging method , the result will be compared with the result that obtained by numerical technique that is fourth order Runge-Kutta method. In this study will be chosen frequency of simple linear pendulum equals one. The result s are averaging method has good accuration for small epsilon values but it decreases for big epsilon values at the specified time

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