Q3 [20 pts] The system in the figure is governed by the equations below assuming the...

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Q3 [20 pts] The system in the figure is governed by the equations below assuming the springs k and k2 have intrinsic damping C1 and C2: Mo sin ot k1 J + k12 0 PBS SOK SD-] m 0 C12 + JO C21 C220 m k2 C k21 k22 0 The solutions to the eigenvalue problem for the above equations, [2M+K] D=0, are given as: first natural frequency is 3.272 Hz and second natural frequency is 6.321 Hz. The transformation matrix, U, constructed with mass-normalized eigenvectors is: 0.7071 U = [1, 2] = [0.7071 , 0.4082 -0.4082 The applied torque is M2(t) = 5sin(@t) Nm. (1 and 2 are 2%. Assume small angle rotation and proportional damping condition. The excitation frequency is at 3 Hz. a. (10 pts) Find the equations of motion (EOM) in matrix form in physical coordinate using the modal approach. b. (10 pts) Find the steady state responses xp(t) and Op(t). Q3 [20 pts] The system in the figure is governed by the equations below assuming the springs k and k2 have intrinsic damping C1 and C2: Mo sin ot k1 J + k12 0 PBS SOK SD-] m 0 C12 + JO C21 C220 m k2 C k21 k22 0 The solutions to the eigenvalue problem for the above equations, [2M+K] D=0, are given as: first natural frequency is 3.272 Hz and second natural frequency is 6.321 Hz. The transformation matrix, U, constructed with mass-normalized eigenvectors is: 0.7071 U = [1, 2] = [0.7071 , 0.4082 -0.4082 The applied torque is M2(t) = 5sin(@t) Nm. (1 and 2 are 2%. Assume small angle rotation and proportional damping condition. The excitation frequency is at 3 Hz. a. (10 pts) Find the equations of motion (EOM) in matrix form in physical coordinate using the modal approach. b. (10 pts) Find the steady state responses xp(t) and Op(t).