Numerically integrate and plot the response of an underdamped system determined by m = 150 kg and k = 4000 N/m, subject to the initial conditions of x0 = 0.01 m and v0 = 0.1 m/s, and the applied force F(t) = 15 cos 10t, for various values of the damping coefficient.
Use this "program" to determine a value of damping that causes the transient term to die out within 3 seconds. Try to find the smallest such value of damping remembering that added damping is usually expensive.