3. Answer the following questions (a) In a two-degree spring mass system with masses my and m2, the equations of motion are: mix , = -(k, +k2)x,+ k2x2 m2x2 = k2x, -k2x2 If the natural frequency @ is related to acceleration by x, = -w x, (i=1, 2), show that the system is a general eigenvalue problem. Convert the problem to a standard eigenvalue problem. If the objects are disturbed from their static equilibrium positions, calculate the natural frequencies (@) of the system if my =0.5 kg, m2 =0.5 kg and k1 =500 N/m and k2 =500 N/m. (20 marks) (b) For a standard eigenvalue problem 2 0 0 - 1 = 1 0 0 X , 0 2 X3 X 3 Find the eigenvalues ^ and the corresponding eigen-vectors. (30 marks)