| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Accurate Period Approximation for Any Simple Pendulum Amplitude |
| XUE De-Sheng,ZHOU Zhao,GAO Mei-Zhen** |
| Key Lab for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 |
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| Cite this article: |
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XUE De-Sheng, ZHOU Zhao, GAO Mei-Zhen 2012 Chin. Phys. Lett. 29 044601 |
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Abstract Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed. Based on an approximation of the elliptic integral, two new logarithmic formulae for large amplitude close to 180° are obtained. Considering the trigonometric function modulation results from the dependence of relative error on the amplitude, we realize accurate approximation period expressions for any amplitude between 0 and 180°. A relative error less than 0.02% is achieved for any amplitude. This kind of modulation is also effective for other large-amplitude logarithmic approximation expressions.
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Received: 05 September 2011
Published: 04 April 2012
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| PACS: |
46.15.Cc
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(Variational and optimizational methods)
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45.50.Dd
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(General motion)
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