Approximation expressions for the large–angle period of a simple pendulum revisited
D. Amrani, P. Paradis and M. Beaudin
Service des Enseignements Généraux, École de Technologie Supérieure, University of Quebec; 1100, Rue Notre–Dame Ouest, Montreal (QC) H3C 1K3, Canada, Tel: (514) 396 8583, Fax: (514) 396 8513 , e–mail: damrani@seg.etsmtl.ca
Recibido el 30 de julio de 2007
Aceptado el 18 de septiembre de 2007
Abstract
This paper presents the experimental accuracy performance of each of the approximation expressions relative to the exact period for large amplitudes of a simple pendulum in the interval 0° < θ < 180°. The plots of the linearized exact period as a function of linearized formulae were carried out and relative errors in these expressions were investigated. In addition, this paper gives a clear idea how each formula approximates the exact period.
Keywords: Large amplitude; simple pendulum; approximation expressions; exact period; linearization; laboratory experiment.
Resumen
Este artículo presenta la eficacia sobre la precisión experimental de cada una de las expresiones de aproximaciones con relación al periodo exacto de grandes amplitudes de un péndulo simple en el intervalo 0º < θ < 180°. Las curvas del periodo exacto linealizado en función de las ecuaciones de aproximaciones linealizadas han sido desarrolladas y los errores relativos de estas expresiones han sido estudiados. Además, este artículo da una idea clara de como cada fórmula se acerca del periodo exacto.
Descriptores: Grandes amplitudes; péndulo simple; expresiones de aproximaciones; periodo exacto; experiencia de laboratorio.
PACS: 01.40. FK
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Acknowledgments
The authors would like to thank Luc Favreau, head of the S.E.G., École de Technologie Supérieure, for his encouragement and support in the development of CBL experiments and demonstrations. We also wish to thank Anne–Marie Fortin, Fernando Avendano, and J.P. Robillard for their help in Spanish translation and computer support, respectively.
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