Calculation of Period of Pendulum:Simple Pendulum.

Keyword

Physics Formulas,Period,Simple Pendulum,Length of Inextensible cord,Acceleration of Gravity,Maximum Angular Displacement.

Reference

[1]:Graham Woan著・堤正義訳:『ケンブリッジ物理公式ハンドブック』,共立出版,pp.74,2007.
[2]:Robert A.Nelson・M.G.Olsson:『The pendulum - Rich physics from a simple system』,American Journal of Physics Vol.54 No.2,February 1986.
[3]:Pendulum:Wikipedia

Remarks

・In the calculation process of the period, air resistance,friction,mass of wire and size of bob are disregarded.
・LaTeX: \\T=T_{0}\left ( 1 +\frac{\Delta T}{T_{0}}\right )\\T_{0}=2\pi \sqrt{\frac{l}{g}}\\\frac{\Delta T}{T_{0}}\\=\sum_{n=1}^{\infty }\left ( \frac{\left ( 2n \right )!}{2^{2n}\left ( n! \right )^{2}} \right )^{2}\sin^{2n}\left ( \frac{\theta _{0}}{2}\right )\\=\frac{1}{16}\theta^{2} _{0}+\frac{11}{3072}\theta^{4} _{0}+\frac{173}{737280}\theta^{6} _{0}+\frac{22931}{1321205760}\theta^{8} _{0}+\cdots
・Making above Equation Image is powered by CODECOGS

History

・2010/04/03:Upload.