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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 as k and c. The car's body

mass is defined as m. Assume that the input from the ground is r(t) = sinot.

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(a) [30 pts] The displacement of the car in s-domain is defined as X(s) = G(s)

the magnitude of the frequency response (G(jw). 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)

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I

(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)

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