I still don''t entirely understand what you want to do, but dampening in the sense of spring/damper systems is given as the dampening value * the velocity.

One of many sites that can shed more light on this:
http://mathinsite.bmth.ac.uk/applet/msd/msd.html

(look up spring/damper systems. In a spring simulation, most apps use numerical integration. With simple 1D motion, the inverse laplace transform will give you a tidy equation based on time, but I don''t know if this applies to your problem)

Author, "Real Time Rendering Tricks and Techniques in DirectX", "Focus on Curves and Surfaces"