Consider the system shown where m = 50 kg, c = 200 N.s/m, k_1 = 350 N.m, and k_2 = 550 N.m. The free end of the spring k_2 is excited by y(t) = 0.4 sin 3t (m) as shown. a) Determine the equation of motion of the system. b) Determine the natural frequency and damping ratio of the system. c) Using ode45 of MATLAB, simulate and plot the response x(t) of the system with initial conditions x(0) = -0.1 m and x(0) = 0.2 m/s. In your simulation use t_final = 15 s. Consider the system shown where m = 50 kg, c = 200 N.s/m, k_1 = 350 N.m, and k_2 = 550 N.m. The free end of the spring k_2 is excited by y(t) = 0.4 sin 3t (m) as shown. a) Determine the equation of motion of the system. b) Determine the natural frequency and damping ratio of the system. c) Using ode45 of MATLAB, simulate and plot the response x(t) of the system with initial conditions x(0) = -0.1 m and x(0) = 0.2 m/s. In your simulation use t_final = 15 s