Chapter 6, Problem 25T

The angular displacement $\theta$ (in radians) for a simple pendulum is given by. $\theta =0.14\sin \frac{\pi }{2}t$ .

a. Determine the period of the pendulum.

b. How many swings are completed in $1\sec$ ?

c. To the nearest degree, what is the maximum displacement of the pendulum?

d. The length $L$ of a pendulum is related to grain the $T$ by the equation $T=2\pi \sqrt{\frac{L}{R}}$ , where, $g$ is the acceleration due to gravity. Find the length of the pendulum to the nearest foot $\left(g=3{\text{2 ft/sec}}^{\text{2}}\right)$ .