The motion of a damped system is described by the following differential equation.
mdt2d2x​+cdtdx​+kx=0 x is the displacement of the mass, t is time (s), and c is the damping coefficient. For c1​=5 the system is underdamped, for c2​=40 the system is critically damped, and for c3​=200 this sytem is overdamped. The initial velocity is 0 and the initial displacement is x=1 m. The mass is 10 kg and k is 40 N/m. Re-write the differential equation as a set of ordinary differential equations. Solve the system from time 0 to 15 with 100 equally spaced elements for each value of c. Name each displacement vector x1,x2, and x3. Plot displacement versus time for each value of the damping coefficient on one graph named h.