The sprung parts of a vehicle weigh $9\mathrm{.}79$ kN$,$ its center of gravity is $106\mathrm{.}7$ cm behind the front axle, and the wheelbase is $228\mathrm{.}6$ cm$.$ The combined stiffness of the springs of the front suspension is $24\mathrm{.}52$ kN$/$m and that of the rear suspension is $26\mathrm{.}27$ kN$/$m $.$ The radius of gyration of the sprung parts about a horizontal transverse axis through the center of gravity is $102\mathrm{.}6$ cm $(40\mathrm{.}4$ in$.).$

$5.$What should be the front and rear damping constants so as to have a damping ratio of $0\mathrm{.}3$ for the quarter car models?

$6.$Determine the parameters of the roll and bounce half car model.

$7.$Calculate body bounce and roll frequencies based on the roll and bounce half car model

$8.$Estimate static suspension deflections $($at the front and at the rear$)$ if four people are to be seated in the vehicle.

$9.$Derive a $1/8$ vehicle model and obtain the transfer function from road vertical speed to sprung acceleration.