摘要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.
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.
XUE De-Sheng,ZHOU Zhao,GAO Mei-Zhen**. Accurate Period Approximation for Any Simple Pendulum Amplitude[J]. 中国物理快报, 2012, 29(4): 44601-044601.
XUE De-Sheng,ZHOU Zhao,GAO Mei-Zhen**. Accurate Period Approximation for Any Simple Pendulum Amplitude. Chin. Phys. Lett., 2012, 29(4): 44601-044601.
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