Damped sine wave The graph of f(t) = e−kt sin t with k > 0 is called a damped sine wave...

Damped sine wave The graph of f(t) = e−kt sin t with k > 0 is called a damped sine wave; it is used in a variety of applications, such as modeling the vibrations of a shock absorber.

a. Use a graphing utility to graph f for , and  to understand why these curves are called damped sine waves. What effect does k have on the behavior of the graph?

b. Compute f′(t) for k = 1 and use it to determine where the graph of f has a horizontal tangent.

c. Evaluate  by using the Squeeze Theorem. What does the result say about the oscillations of a damped sine wave?