Higher accurate approximate solutions for the simple pendulum in terms of elementary functions

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Title: Higher accurate approximate solutions for the simple pendulum in terms of elementary functions
Authors: Beléndez, Augusto | Francés, Jorge | Ortuño, Manuel | Gallego, Sergi | Bernabeu, Guillermo
Research Group/s: Holografía y Procesado Óptico | GITE - Física, Óptica y Telecomunicaciones
Center, Department or Service: Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal | Universidad de Alicante. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías
Keywords: Nonlinear pendulum | Period | Approximate solution | Tension
Knowledge Area: Física Aplicada
Date Created: 1-Mar-2010
Issue Date: 28-Apr-2010
Editors: Institute of Physics Publishing
Citation: BELÉNDEZ VÁZQUEZ, Augusto, et al. "Higher accurate approximate solutions for the simple pendulum in terms of elementary functions". European Journal of Physics. Vol. 31, No. 3 (2010). ISSN 0143-0807, pp. L65-L70
Abstract: A closed-form approximate expression for the solution of a simple pendulum in terms of elementary functions is obtained. To do this, the exact expression for the maximum tension of the string of the pendulum is first considered and a trial approximate solution depending on some parameters is used, which is substituted in the tension equation. We obtain the parameters for the approximate by means of a term-by-term comparison of the power series expansion for the approximate maximum tension with the corresponding series for the exact one. We believe that this letter may be a suitable and fruitful exercise for teaching and better understanding nonlinear oscillations of a simple pendulum in undergraduate courses on classical mechanics.
Sponsor: This work was supported by the “Vicerrectorado de Tecnología e Innovación Educativa” of the University of Alicante, Spain (GITE-09006-UA).
URI: http://hdl.handle.net/10045/13911
ISSN: 0143-0807 (Print) | 1361-6404 (Online)
Language: eng
Tipe: info:eu-repo/semantics/article
Rights: Copyright © IOP Publishing Ltd
Publisher version: http://dx.doi.org/10.1088/0143-0807/31/3/L04
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