Chapter 4.8, Problem 45E

Applications

45. A damped oscillator The displacement of a particular object as it bounces vertically up and down on a spring is given by y(t) = 2.5e^−t cos 2t, where the initial displacement is y(0) = 2.5 and y = 0 corresponds to the rest position (see figure).

1. a. Find the time at which the object first passes the rest position, y = 0.
2. b. Find the time and the displacement when the object reaches its lowest point.
3. c. Find the time at which the object passes the rest position for the second time.
4. d. Find the time and the displacement when the object reaches its high point for the second time.