A certain car has suspension modes which are uncoupled front to back.  When a person with a mass of 60 kg sits in the rear of a car, in the centre of the seat which is directly over the wheel arch, the rear suspension deflects 5 cm. 

The natural frequency of the unloaded car body on the rear suspension is 1.6 Hz. The damping factor ζ is 0.3.

The rear wheels each have a combined imbalance equivalent to 30 gm at 40 cm eccentricity.  The wheel diameter is 0.6 m.  

(a) What is the combined stiffness of the rear suspension springs of this car?

(b) What is the effective body mass associated with the rear suspension?  (Ignore the mass of occupants.)

(c) Assuming linearity, evaluate the damping coefficient of each of the rear dampers?

(d) The wheel hop frequency for the rear suspension is 15 Hz.  At what road speed would the imbalance of the rear wheels induce resonance?  

(e) What is the force due to wheel imbalance when the car is travelling at 80 kph?