# Period of the pendulum (table)

## 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 ]
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt

 $\normal Period\ of\ the\ pendulum\\(1)\ T=4\sqrt{\large\frac{l}{g}}{\large\int_{\small 0}^{\hspace{25}\frac{\pi}{2}}\frac{d\phi}{\sqrt{1-sin^2({\large{\frac{\alpha}{2}}})sin^2\phi}}}\\\hspace{40}=4\sqrt{\large\frac{l}{g}}K(sin{\large\frac{\alpha}{2}})\\[10]\hspace{25} K:\ 1st\ complete\ elliptic\ integral\\[10](2)\ approximation\\\hspace{25} T_0 =2\pi\sqrt{\large\frac{l}{g}}\simeq T\\$

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