A heavy machine tool mounted on the first floor of a building, Figure DP2 (a), has been modeled as a three-degree-of-freedom system as indicated in the Figure DP2 (b). (a) For k, = 900 kN/m, k₂ = 900 kN/m, k3 = 3.5 MN/m, c, = C2=C3 = 2,000 N-s/m, my = 9,000 kg, m, 1,800 kg, m = 380 kg, and F(t) = 200 cos 60t N, find the steady- state vibration of the system using the mechanical impedance method. (b) If the maximum response of the machine tool head (x3) has to be reduced by 20 percent, how should the stiffness of the mounting (k) be changed? (c) Is there any better way of achieving the goal stated in (b)? Provide details. Wall Mounting Machine tool head (equivalent mass, m) F(t), cutting force Machine tool base (equivalent mass, m) (a) F(t) Floor (equivalent mass, my) m X3(1) 1 Machine tool head k3 Cz X2(1) ть Base and mounting k₂ C₂ x₁(1) my Floor k₁ (b) Figure DP2