Problem on damping coefficient

Vertical suspension system of a car can be modeled as single degree of the freedom system. Consider that the car with mass m consists of four shock absorbers with equal stiffness and damping of k and c, corresspondingly:

(a) Due to self-weight of the car, the suspension system is deflected by 0.03m. The suspension is made to be critically damped. If the car has a mass of 1530 kg, calculate the equivalent damping coefficient of the suspension system.

(b) Plot the displacement response of the suspension system in part (a). Also plot on the same diagram the responses of the suspension system if the initial velocities are 2 cm/s and -2 cm/s.

(c) If four passengers with the average mass of 70 kg each and luggage of 50 kg are in the car, how does this affect the effective damping ratio? Plot the displacement response of the suspension system on the same plot in part (b) and comment the vibration characteristic of the car with passengers and luggage.

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