A simple pendulum whose length l = 9.8 m satisfies tire equation(a) If Θ0 is the amplitude...

A simple pendulum whose length l = 9.8 m satisfies tire equation

(a) If Θ0 is the amplitude of oscillation, show that its period T is given by

 where α = sin2 1/2 Θ0

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(b) Expand tire integrand in powers of a, integrate term by term, and find the period T as a power series in α. Keep terms up to and including O(α2).

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(c) Expand α in a power series of Θ0 insert the result into the power series found in (b), and find the period T as a power series in Θ0. Keep terms up to and including 0(Θ02).