PENGARUH VARIASI STEP-LENGTH INTEGRASI PENDULUM NONLINEAR

Effendi, Hansi (2008) PENGARUH VARIASI STEP-LENGTH INTEGRASI PENDULUM NONLINEAR. TEKNIKA UNAND, 1 (30). ISSN 0854-8471

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Abstract

This paper is to investigate the effect of varying the integration step-length, T, of non-linear pendulum. The non-linear model is derived from a simple forced pendulum with point mass m and rod length l. The model is solved iteratively. The tricky part of this equation is to predict the next output in order to find the next output. The best prediction for the next output will be the current output. At every loop, the answer provided by the equation is used as the predicted output for the next loop. This step is repeated until the predicted output and the actual output is equal to each other. It is surprisingly that, it only takes a few loops to produce the correct output if the time step is small enough. With small time step, the next output will be close to the current output. Hence, it is reasonable to use the current output as the expected next output providing the time step is very small. It is obvious that the number of step to produce a correct output and the error of the numerical integration increase rapidly with increasing time step size. Keywords: Nonlinear pendulum, step-length, iterative, numerical integration

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