A partially loaded passenger car has a mass of 1600 kg.  It has fully independent suspension in which each front spring has a stiffness of 19.0 kNm^-1 and each rear spring has a stiffness of 17.0 kNm^-1.

The car has a wheelbase of 2.9 m and the centre of gravity is 1.6 m in front of the rear wheels.  The radius of gyration of the sprung mass about a horizontal transverse axis through the centre of gravity is 0.95 m.

Model the car as a linear, undamped, 2 degree of freedom system, ignoring tyre stiffness, and calculate:

(a)  The natural frequencies for the two modes of vibration.                      

(b) The positions of the pitch centres for each of these modes relative to the centre of gravity.