Problem 3: (%20) Consider the following rotational and translational mechanical system and the free body diagram of the bar. Assume that the spring is unstreched when is zero and is small. Let m = 0.6 kg, k = 10 N/m, L = 0.8 m, c = 6 N/(m/s), Jo= = m 3 = 0.128 kg m2. L m 2k www www 3m KO x(t) T(t). T(t) 5/8 L 3k L 3k/510) m c(x-1)+2k (x-1) a) By using the translational equation of motion for the mass 3m, show that the transfer 4.8 s +16 function X(s)/(s) is given by X(s) (s) = 1.8 s + 6s+30 b) Obtain the rotational equations of motion for the the bar.