(b) A bar of length 3a and of moment of inertia about O, I, is supported by a linear spring and a dashpot damper as illustrated in Fig Q1b. The bar pivots about the hinge at O. Assuming that the bar can only move through small angles, derive an equation of motion for the system. [3] = The bar is given an initial displacement in the clockwise direction of 3 and is released from rest. If the distance a = 0.53 m, the spring stiffness is k 1150 N/m, the damping coefficient is c = 7400 Ns/m and the moment of inertia is lo = 318 kgm. Calculate the damping ratio, 3, of the system. [3] Hence, determine an expression for the rotational response of the system with time, e(t). [10] a 2a Figure Q1b k 70