Question 5 (45 points) Imagine that you design a suspension for a car described below. There are four suspensions in the car and total stiffness and damping coefficients are defined ask and c. The car's body mass is defined as m. Assume that the input from the ground is r(t)=sina. k e (a) [30 pts] The displacement of the car in s-domain is defined as X(s)-G(s) Find the magnitude of the frequency response |G(ja). Draw it in the frequency domain with various . Please show all the procedures including the equation of motion, free body diagram, transfer function, and magnitude. (Show all the procedures) (b) [15 pts] Our goal is to minimize the effect of ground vibration after the resonance peak by designing the suspension (k, c) or the car's body mass (m). Please explain how to design each parameter (k, c, m) to reduce the magnitude after the resonance peak. (Show all the procedures)

Fig: 1