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Pendulum Period

TOP/Collection of Physics Formulas/Vibration
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Calculate the period of a pendulum.
Angle α at rest
°
String length l
m
[Gravitational acceleration g
m/s2]
Pendulum Period T  seconds
\(\normalsize Period\ of\ the\ pendulum\\ (1)\ T=4\sqrt{\large\frac{l}{g}}{\large\int_{\small 0}^{\frac{\pi}{2}}\frac{d\phi}{\sqrt{1-sin^2({\large{\frac{\alpha}{2}}})sin^2\phi}}}\\ \hspace{40px}=4\sqrt{\large\frac{l}{g}}K(sin{\large\frac{\alpha}{2}})\\ \hspace{25px} K:\ 1st\ complete\ elliptic\ integral\\\)

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