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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

Increment

of pendulum angle α

[ Gravity g

m/sec² ]

Angle α	Period T	Approximation T0	T/T0

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

Period of the pendulum (table)

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

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