Comparison of the Analytical Semi-Solution of the Differential Equation of Simple Harmonic Motion with the Solution obtained using the Runge- Kutta-Fehlberg Method
Marco Aurélio Amarante Ribeiro
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José Helvécio Martins
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Resumo: The solution of the differential equation describing simple harmonic motion, represented by a classical pendulum, was discussed. The results of an analytical solution presented in the literature were compared with the results obtained with the Runge-Kutta-Fehlberg method. It was concluded that, practically, there is no difference between the results of these two solutions. A linearized solution has also been considered. This confirms that this solution is valid only for very small amplitudes. Furthermore, the discussions show that the analytical solution presented in the literature cannot be expressed in terms of elementary functions. Therefore, this solution must be considered semi-analytic, as no solution expressed in terms of purely elementary functions has been found in the literature. In this context, it might be interesting to look for such a solution or, perhaps, to demonstrate in detail that this solution can be solved with very good precision using a robust numerical technique.
Palavras-chave: Simple pendulum, Harmonic motion, Semi-analytical solution, Elliptic integrals, Runge-Kutta-Fehlberg.
Edição: Vol. 3 - Núm. 1 | DOI: 10.5281/zenodo.7741020
