# Period of the pendulum (table) Calculator

## Calculates a table of the exact and approximate periods, and relative period ratios of the pendulum.

 String's length l m Increment 5° 10° of pendulum angle α [ Gravity g m/sec2 ] 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Period\ of\ the\ pendulum\\(1)\ T=4\sqrt{\large\frac{l}{g}}{\large\int_{\small 0}^{\hspace{25}\frac{\pi}{2}}\frac{d\phi}{\sqrt{1-sin^2({\large{\frac{\alpha}{2}}})sin^2\phi}}}\\\hspace{40}=4\sqrt{\large\frac{l}{g}}K(sin{\large\frac{\alpha}{2}})\\[10]\hspace{25} K:\ 1st\ complete\ elliptic\ integral\\[10](2)\ approximation\\\hspace{25} T_0 =2\pi\sqrt{\large\frac{l}{g}}\simeq T\\$

Period of the pendulum (table)
 [1-1] /1 Disp-Num5103050100200
[1]  2014/02/26 02:20   Male / 40 years old level / A teacher / A researcher / Very /
Purpose of use
Teaching 1st year physics students about pendula at the University of Toronto.
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