Expanding the integrand in Eq. (19.19) of Sec. 19.4 into a
Chapter 19, Problem 19.33(choose chapter or problem)
Expanding the integrand in Eq. (19.19) of Sec. 19.4 into a series of even powers of sin w and integrating, show that the period of a simple pendulum of length l may be approximated by the formula
\(\mathrm{t}=2 \mathrm{p}_{\mathrm{B}} \frac{\bar{l}}{\bar{g}}\left(1+\frac{1}{4} \sin ^{2} \frac{\mathrm{u}_{m}}{2}\right)\)
where \(u_{m}\) is the amplitude of the oscillations.
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