Please show step by step calculations (by hand).

The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation dx dx dtdt where x displacement from equilibrium position (m) t- time (s), m 20-kg mass, and c the damping coefficient (Ns/m). The damping coefficient c takes on three values of 5 (underdamped), 40 (critically damped), and 200 (overdamped). The spring constant k 20 N/m. The initial velocity is zero, and the initial displacement x 1 m. Solve this equation using a numerical method over the time period 0 sts 15 s. Plot the displacement versus time for each of the three values of the damping coefficient on the same curve. FIGURE P25.16 1n2