Start with a real spring of length L made from a wire with a total length 10 L and a spring constant k. In a real system, the motion will eventually decay.
Biological tissues are elastic too.
If you pinch out your skin a little, it will return to its resting position quite rapidly. But it usually won't oscillate. A typical molecular motor can exert a force of 2 pN over a distance of approximately 10 nm. A typical cell in the blood has a diameter of around 20 microns, and when attached to a surface like the wall of the blood vessel, can move around 10 microns per minute.