Equation (5), (6), (7) and (8) indicates the sprung mass transmissibility, un-sprung mass transmissibility, sprung
mass deflection, and tyre deflection respectively. To optimize the suspension system, plots of time response of
equations (5), (7), (8) and frequency response of equations (5), (6) are plotted as shown in Fig 9 and Fig 10. From
the time response, the range of damping ratio is selected in order to have damped state with the required time. In
case of race cars, the damping should be fast enough to damp the oscillations in 0.2 to 0.5 seconds, hence a range of
damping ratio [0.4 0.8] is selected (Fig 9). The frequency response of equations (3) and (4) are plotted across this
selected range of damping ratio. Since, the rider comfort decreases with the increase in acceleration of the body, the
amplitude of acceleration of the sprung mass was to be minimize. The peak amplitude of the wheel displacement at
both the fundamental frequencies of un-sprung mass to be minimize in order to make sure that the wheel does not
lose contact with the ground. As damping ratio of the damper increases, acceleration of sprung mass decreases; but
at the same time un-sprung mass transmissibility also increases which may lose tyre contact with ground. Hence we
need to select optimum damping ratio. Literature [17] states that, the damping ratio is optimum when the plot (Fig
10) across to resonance frequencies becomes almost linear so as to have less jerk at resonating frequencies. As
shown in Fig 10, for damping ratio 0.7 the graph between the two natural frequencies becomes almost straight line.
Hence the damping ratio becomes q = 0.7. Coefficient of damping is obtained which is, C = 0.7Co, where Co is the