Mechanical Vibrations HW Use the modal analysis and numerical integration to compute and plot the time response of the system, which has the equations of motion [8 0 01 (1) 48 -12 01(x1 0 0 8 02-12 48 -12 x2 = 5 sin 3t LO 0 18 (3) 0 -12 48 (x3) 10 sin 9t) subject to the initial conditions x(0) = = 0,x (0) = 0.1. Assume modal damping of the form = 32 = 3 = 0.02