Chapter 6.1, Problem 21E

Oscillating motion A mass hanging from a spring is set in motion, and its ensuing velocity is given by v(t) = 2π cos πt, for t ≥ 0. Assume that the positive direction is upward and that s(0) = 0.

1. a. Determine the position function, for t ≥ 0.
2. b. Graph the position function on the interval [0, 4].
3. c. At what times does the mass reach its low point the first three times?
4. d. At what times does the mass reach its high point the first three times?