Chapter 7.4, Problem 33PE

The angular displacement 6 (in radians) of a pendulum swinging through a small angle with limited air resistance and Internal friction can be approximated by the simple harmonic motion models $\theta =a\sin \omega t$ or $\theta =a\cos \omega t$ . The period T (time required for one back-and-forth swing) Is given by $T=2\pi \sqrt{\frac{L}{g}}$ , where L is the length of the pendulum and g is the acceleration due to gravity. The maximum angular displacement is al and positive angles are taken to the right of the center position. Use this information for Exercises 33-34.

33. A 4-ft pendulum is initially at its right-most position of 12°.
a. Determine the period for one back-and-forth swing. Use g = 32 ft/sec².
b. Write a model for the angular displacement $\theta$ of the pendulum after t seconds, (Hint: Be sure to convert the initial position to radians.)