I know this is nit picking, but dampening is getting something wet. Damping is prolonging a moment of force.
I used the word DAMPEN, as in the shock absorber will DAMPEN the oscillation of the spring or restrict the motion of the spring. Definitions: 1. to make damp (you are right here)
2. to deaden, restrain, or restrict
3. to soundproof
Small point- if you dampen the motion you, do not prolong the motion. When you dampen the motion you reduce or restrict the oscillations