*The Influence of Damping on Free Response*

Shown below are three time histories for the free response of a single-DOF system with zero initial stretch in the spring and an initial velocity downward. These time histories correspond to damping ratios of 0, 0.1 and 0.5. (Recall that for oscillations to exist in the free reponse, the damping ratio must be less than one.) The most obvious influence of an increase of damping is the decay of the amplitude of the oscillations in time. In addition, the period of the decaying oscillations increases as the damping ratio is increased.

Shown below is the influence of the damping ratio on the free response of the single-DOF system for the range of the damping ratio from zero to one. Note how quickly the free response dies away for even small amounts of damping (0.1 to 0.2 damping ratio).

**(ANIMATION REPLAYS CONTINUOUSLY)**