Consider the example of the automobile drive train system discussed in Problem 4.47, modeled by 75 0 0 1 -1 0 0 100 0 x+10,000 -1 3 -2x=0 0 0 3000 0 -2 2 x(0) = 0 and x(0) = [001] m/s Add 10% modal damping to each coordinate, calculate and plot the system response. REFERENCE: 4.47. A vibration model of the drive train of a vehicle is illustrated as the three-degree-of- freedom system of Figure P4.47. Calculate the undamped free response [i.e., M(t) = F(t) = 0, c₁ = c2 = 0] for the initial condition x(0) = 0, x(0) = [001]. Assume that the hub stiffness is 10,000 N/m and that the axle/suspension is 20,000 N/m. Assume the rotational element J is modeled as a translational mass of 75 kg. Rotational Tire damping Hub damping x₁(t) x2(1) x3(1) M(t) Clutch torque Torque convertor inertia Equivalent inertia of transmission Vehicle equivalent inertia F(t) -Wind and J=75 kg-m²/rad road load m2=100 kg m3=3000 kg Hub stiffness Axle and suspension stiffness Translational Figure P4.47 A simplified model of an automobile for vibration analysis of the drive train. The parameter values given are representative and should not be considered as exact.