Chapter 4.5, Problem 6SP

A mechanical metronome uses an inverted pendulum that makes a regular, rhythmic click as it swings to the left and right. With each swing, the pendulum moves $3\text{ in}$ . to the left and right of the center position. The pendulum is initially pulled to the right $3\text{ in}$ . and then released. It returns to its starting position in $0.8$ sec. Assuming that this pattern continues indefinitely and behaves like a cosine wave, write a function of the form $x\left(t\right)=A\cos \left(Bt-C\right)+D$ . The value $x\left(t\right)$ is the horizontal position (in inches) relative to the center line of the pendulum.