5. A 2-DOF linear elastic structure, with mass matrix m = [4000 5000 kg, and stiffness matrix k = Questions: -3000 103 N/m, external load p = 103 (30) sin5t N. (10 points) 300 -300 800 (1) Determine the vibration modes and natural frequency of the system; (2) Proof the orthogonality features of the vibration modes (3) Suppose the structure's response can be expressed by modal superposition method as v = Y, Y= (1), where is the vibration mode matrix, give the steady state response of the system (hint: calculate Y and Y2 first)