| Título: | Reply to ‘Comment on “Approximation for the large-angle simple pendulum period”’ |
| Autores: |
Beléndez Vázquez, Augusto Rodes Roca, José Joaquín Beléndez Vázquez, Tarsicio Hernández Prados, Antonio |
| Fecha: |
2009-09-03 2009-09-03 2009-06-05 2009-08-03 |
| Publicador: | RUA Docencia |
| Fuente: |
 |
| Tipo: | info:eu-repo/semantics/article |
| Tema: |
Simple pendulum Large amplitudes Approximate period Física Aplicada |
| Descripción: |
In their comment, Qing-Yin and Pei derived another analytical approximate expression for the large-angle pendulum period, which they compare with other expressions previously published. Most of these approximate formulas are based on the approximation of the original nonlinear differential equation for the simple pendulum motion. However, we point out that it is possible another procedure to obtain an approximate expression for the period. This procedure is based on the approximation of the exact period formula —which is expressed in terms of a complete elliptic integral of the first kind— instead of the approximation of the original differential equation. This last procedure is used, for example, by Carvalhaes and Suppes using the arithmetic-geometric mean. The authors thank to Claudio G. Carvalhaes for send us their papers about the nonlinear pendulum and the arithmetic-geometric mean. This work was supported by the “Vicerrectorado de Tecnología e Innovación Educativa” of the University of Alicante, Spain (GITE-09006-UA). |
| Idioma: | Inglés |
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