Chapter 8.5, Problem 50AE

In Problems 45-50. the distance $d$ (in meters) of the bob of a pendulum of mass $m$ (in kilograms) from its rest position at time $t$ (in seconds) is given. The bob is released from the left of its rest position and represents a negative direction.

(a) Describe the motion of the object. Be sure to give the mass and damping factor.

(b) What is the initial displacement of the bob? That is, what is the displacement at $t=0$?

(c) Graph the motion using a graphing utility.

(d) What is the displacement of the bob at the start of the second oscillation?

(e) What happens to the displacement of the bob as time increases without bound?

$d=-10e^{-0.8t/50}\cos \left(\sqrt{{\left(\frac{2\pi }{3}\right)}^2-\frac{0.64}{2500}}t\right)$