Chapter 7, Problem 137RE

For the following problem, set up and solve the differential equation.

137. The motion of a swinging pendulum for small angles $\theta$ can be approximated by $\frac{d^2\theta }{d{t}^2}+\frac{g}{L}\theta =0$ , where $\theta$ is the angle the pendulum makes with respect to a vertical line, g is the acceleration resulting from gravity, and L is the length of the pendulum. Find the equation describing the angle of the pendulum at time t, assuming an initial displacement of ${\theta }_0$ and an initial velocity of zero.