As shown in the following figure, a system contains a mass, two springs, and a viscous damper c. The motion of the right end (point A) of the damper is prescribed as y(t) = Y sin wt. (a) Obtain the governing equation; (15 points) (b) Find the amplitude X of x(t) (consider the particular response only); (10 points) (c) If other parameters are fixed while can be freely chosen, does the maximum response of X occur at w = wn1-23 (where wn is the natural frequency and is the damping ratio), as predicted in the standard system? Give your explanation (10 points) Note: The parameters m, c, k, Yo are given. Assume that the system is underdamped. y = Y sin wt k www k in X m I C