To determine the motion of the body as well as the spring and damper forces during arbitrary excitation (e.g. a measured road surface profile) computers are most suitable, particularly when non-linear characteristics (e.g. tire lift off, deflected shock-absorber and spring characteristics) are to be considered.
If a sinusoidal wave is used (sinusoidal signal of constant amplitude and varied frequency) as an excitation signal, the amplification function can be determined from the peak values of body amplitude and excitation amplitude
Note: The amplification function for the body amplitudes normalised to the excitation amplitudes is identical to the amplification function for body acceleration normalised to the excitation accelerations, as follows from the double differentiation of a sinusoidal oscillation with the frequency
The amplification function of the single mass suspension model is shown in the figure for tire data in as per paragraph 1.2.1.
Due to the negligible self damping behavior of the tires, a pronounced resonance peak occurs. The natural frequency – resulting from proportionate body and axle mass and the tire spring rate – which is approximately 3 - 4 Hz, is situated in a frequency range of high human sensitivity to vibration.