Damping of vibrations in pump
 

Dear All,
I have a question related not directly to CFD, I would like to study the problem in analytical way if possible.
The situation is as follows: there is a test facility for high-pressure valves. The facility consists of the pump (of diameter say 300 mm and heigh of 1000 mm, made of steel with given characteristics), the short connection pipe of diameter of 20 mm and different valves. The piston presses the water in pump in time as long as assumed mass flow is achieved (this time is noticed and is measure of certain valve "efficiency").
The problem under study is damping of the vibrations started by the piston in the moment when it starts to pump. The start of the piston causes the vibration of given period and damping. Problem is to find theoretical way to asses the dampin coefficient (this coeff. can be measured but here I have to try to describe it theoreticaly).
I was trying to find something about damped helmholtz resonators or something (which I thing the pump is in first closure), but without big succes. I would be very grateful if someone can suggest a good literature for calculation of damping of such arrangements (water filled cavities of standard shapes or so). Eventually maybe some computational mechanical approch can be suggested.

I would be very grateful for help,
Lukasz