For the following mechanical system (30 POINTS) a. Derive the differential equation: draw the FBD, use Newton’s laws (4 points) b. Identify the transfer function T(s)=X(s)/F(s) (2 points) c. Find expressions for frequency dependence of gain A(w) and phase Φ (w) (6 points) d. Draw rough semi‐log plots (gain in dB vs. w , phase in degrees vs. w) (10 points) e. What is damping ratio of the coupled system? (2 points) f. If input is f(t)= 1 sin (1t), what is output xss(t)= A