Problem 1. Transfer Function Consider the following mechanical system. the fo (50 Points) Chain the r k2 000000 m b b2 Show that the relationship between u(t) and y(t) can be expressed as: (10 points) (t) + (b +b2)(t) + (k1 + k2)y(t) = u(t) Obtain the transfer function G(s) = = Y(s) U(s)' (10 points) Let m = k2 = 0.5 [N/m]. Also, let y(0) 1 [m], 1 [kg], b = b2 = 1 [N.s/m], and k = k2 y(0) = 1 [m/s], and u(t) = 1, t 0 (i.e., u(t) is the step function). Obtain the response of the system. = (30 points)