Suppose that the mass in a mass-spring-dashpot system with m = 10, c = 9, and k = 2 is set...

Suppose that the mass in a mass-spring-dashpot system with m = 10, c = 9, and k = 2 is set in motion with x(0) = 0 and a′(0) = 5. (a) Find the position function x(t) and show that its graph looks as indicated in Fig. 1. (b) Find how far the mass moves to the right before starting back toward the origin.

FIGURE 1. The position function x(t) of Problem 13.