The subsequent force that we want to consider is damping. This force may or may not be there for any specified problem.

Dampers work to counteract any movement. There are some ways to describe a damping force. The one that we'll utilize is the following.

Fd  = -g u′

Here, g > 0 is the damping coefficient. Let's think for a minute regarding to how this force will act. Whether the object is moving downward, so the velocity ( u′ ) will be positive and therefore F_d will be negative and acting to pull the object back up. Similarly, if the object is moving upward, the velocity (u′) will be negative and therefore F_d will be positive and acting to push the item back down.

Conversely, the damping force as we've described this will always act to counter the recent motion of the object and therefore will act to damp out any motion into the object.