In this paper, the free vibration of a one-degree-of-freedom system with viscous damper supported ellastically and with springs whose stiffness ratio κ is arbitrary, is studied. Some intresting facts have been derived from the study that the system has an optimum damping value for the free vibration and that the value is nearly equal to that for the forced vibration. In addition, the transient nature of a vehicle equipped with a damper adjusted adequately for the steady motion in passing over a raised or sunken place, has been investgated, comparing the result with the conventional type of suspension consisting of a spring connected in parallel with a damper, and it has become clear that the former has considerable advantages in comparison with the latter in reducing shocks.