Damper Types
Over Damper.

Awaiting Photographs.

Over Dampers are as stated over the hammers and in 99% of cases rely on gravity as the damping force. This is very inefficient for two reasons. One. The dampers are close to the edge of the string, not a good place to dampen the string.
Two. Gravity is insufficient a force to efficiently dampen the strings. 
Under Damper. Under Dampers are positioned under the hammers and use springs as the damping force. This puts the damper near the middle of the string. The springs are graded to help match the damping force with the force of the vibration. 
This is the preferred method and is the method used in all new upright pianos