Ubi. (a). (25 points) A mechanical system consists of 3 rigid bodies with Mass M1, M2 and M3, linked by three springs wi

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Ubi A 25 Points A Mechanical System Consists Of 3 Rigid Bodies With Mass M1 M2 And M3 Linked By Three Springs Wi 1 (222.38 KiB) Viewed 52 times

Ubi. (a). (25 points) A mechanical system consists of 3 rigid bodies with Mass M1, M2 and M3, linked by three springs with stiffness K1, K2 and K3. The end of the first spring is fixed to a rigid frame. The bodies move on a frictionless horizontal surface with respective displacements, X1, X2 and X3. (i). Deduce the equations of motion of the 3 bodies (5 Marks) (ii). Assuming Xi = -w2Xi (where w is natural frequency of free oscillation); M3 = 0 and K3 = 0, determine the Eigenvalues and Eigenfunctions of the motion of the remaining two masses. Discuss the mode of oscillations. - - (10 marks) (Take Ki = K2=K; Mi-4175 M2=21) = (b) . = a²x Solve the sirnuitaneous differential equations: + 2x - y = 0 (1) dt2 d²y + 2y - x = 0 (2) dt2 given that at t=0, Xo = 4; yo = 2; x1 = 1; yı = 0 (10 Marks) =