Chapter 8.7, Problem 13P

The exact equation of motion of a simple pendulum is $d^2\theta /d{t}^2=-{\omega }^2\sin \theta$ where ${\omega }^2=g/l.$ By method (c) above, integrate this equation once to find $d\theta /dt$ if $d\theta /dt=$ 0 when $\theta ={90}^{°}.$ Write a formula for $t(\theta )$ as an integral. See Problem 5.34.