By expanding the integrand in Eq. (19.19) into a series of even powers of sin ø and integr...

By expanding the integrand in Eq. (19.19) into a series of even powers of sin ø and integrating, it can be shown that the period of a simple pendulum of length l can be approximated by the expression

Fig. P19.C1

where and θm is the amplitude of the oscillations. Use computational software to calculate the sum of the series in brackets, using successively 1, 2, 4, 8, and 16 terms, for values of θm from 30 to 120° using 30° increments.

 (19.19)