Animate
This plots position (vertical) as a function of time (horizontal) for an object subject to a Hooke's Law restoring force.
Suppose that the object is also subject to a force that always acts opposite the velocity, v, and is proportional to the magnitude of v. If the constant of proportionality is denoted R, then this damping force is -Rv. Investigate the motion for different values of R (say 1, 5, 10, 20).