Answer Happy

m mass of car Velocity of car Consider the single-degree-of- freedom model of an automobile driving over the road shown in the figure. The road surface is approximated as sinusoidal in cross section providing a base motion displacement of y(t) = Y sin wt where Y = 0.01m, Suspension system Neglected unsprung mass 0.02 m -6 m Road surface km W = V " (C) () 3) Cenyele) = 0,29090, hour (2 rad 0.006km/3600s and v denotes the vehicle's velocity in km/h. Assume that the mass of the car m = 1007 kg and c = 2000N.s/m. The above system can be modeled by the block diagram shown in the figure below with response signal z(t) = x(t)- y(t) and sinusoidal input function r(t) = R sin wt where R = mYw2. Therefore, the steady-state response beomes Zss(t) = 2(w) sin(wt + o) =
z(t) r(t) = R sin wt + G(S) 1 ms2 + cs K a) Choose k = 10 and draw the Bode plots (magnitude and phase) of the closed-loop transfer function. b) What is the phase angle when the vehicle moves with velocity 10km/h. c) What is the maximum value of K so that
|2w|_ Z(0) max R R w Zw) d) What is the value of K so that becomes maximum when = 0.6 and the vehicle moves with velocity 20 km/h. R