Chapter 6.4, Problem 54PE

For Exercises 53-54, use the model $d=a{e}^{-ct}\cos \omega t$ or $d=a{b}^{kt}\cos wt$ to represent damped harmonic motion.

A pendulum is pulled $\frac{\pi }{18}$ radians to one side and then released. The angular displacement $\theta$ follows a pattern of damped harmonic motion with each cycle lasting $2\sec$ . If the maximum displacement for each cycle decreases by $20\%$ , find a function that models the angular displacement $t\sec$ after being released.