Problem 2. The motion of a damped springmass system (Fig. P2116) is described by the following ordinary differential equation: 2 mdzx+c+kx= 0 dr2 dt where x = displacement from equilibrium position (m), I: time (s), m = 20kg mass, and c = the damping coefficient (N - sfm). The damping coefficient 5' takes on three values of 5 (underdamped), 40 (critically damped}, and 200 (overdamped). The spring constant k = 20 me. The initial velocity is zero, and the initial displacement at = l m. Solve this equation using a numerical method over the time period 0 E t S 15 5. Plot the displacement versus time for each of the three values ofthe damping coefficient on the same curve. FIGURE P25.16 |>x