Chapter 8.5, Problem 34P

Find the equation of motion of a simple pendulum (see Chapter 7, Problem 2.13), that is, the differential equation for $\theta$ as a function of t. Show that, for small $\theta ,$ this is approximately a simple harmonic motion equation, and find $\theta$ if $\theta ={\theta }_0,d\theta /dt=0$ when $t=0$.