Pendulum Periods (Table)
Compare the pendulum period T with the approximate period T0 and tabulate the ratio T/T0.
| \(\normalsize Period\ of\ the\ pendulum\\ (1)\ T=4\sqrt{\large\frac{l}{g}}{\large\int_{\small 0}^{\frac{\pi}{2}}\frac{d\phi}{\sqrt{1-sin^2({\large{\frac{\alpha}{2}}})sin^2\phi}}}\\ \hspace{45px}=4\sqrt{\large\frac{l}{g}}K(sin{\large\frac{\alpha}{2}})\\ (2)\ T_0 =2\pi\sqrt{\large\frac{l}{g}}\simeq T\\\) |
T: pendulum period, T0: approximate period, K: complete elliptic integral of the 1st kind
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