A competitor in a hill-climb event finds during practice that his car becomes airborne at a particular point on the hill.  Shortly after landing the lowest point in the car just contacts the road.   The mass of the car is 2000 kg and the suspension is designed to give a natural frequency of 1.3 Hz.  The static ground clearance is 100 mm.  The dampers are set to give a damping ratio of 0.3 of critical damping.

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

(b)  What is the damping coefficient of one of the dampers assuming they are identical?

(c)  Determine the minimum ground clearance after impact which would result if the damper settings were increased by 25%. 

You should assume that the car can be treated as a one degree of freedom system for the transient that occurs when it hits the ground.  You should assume that the suspension springs are in their static equilibrium position when the car hits the ground.  You should also assume that after becoming airborne the car always hits the ground with the same downwards velocity.

Note that the transient response for a one degree of freedom system with z < 1 is given by

where   x(0) and x'(0) are the initial displacement and velocity at t = 0.

You may wish to use EXCEL to solve part (c)