Applications of Critical Damping

Factors that affects the damping coefficient b includes the drag in the oscillating spring-mass system that takes energy out of the system as heat loss etc.
therefore, the higher the viscosity of the medium the system is in, the greater the drag coefficient b.

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM21/SHM21_Simulation.xhtml

1) Car suspension

The spring of a car’s suspension is critically damped so that when a car goes over a bump, the passenger in the car quickly and smoothly regains equilibrium.

the picture shows no damping case b = 0

the picture shows light damping case b = 0.1

the picture shows critically damping case b = 2.0
However, car suspensions are often adjusted to slightly under critical damped condition to give a more comfortable ride. Critical damping also leaves the car ready to respond to further bumps in the road quickly.