How to calculate mass needed for mounting electrodynamic vibration shaker?

Contacting the manufacturer is a good idea. The mounting and safety considerations will depend on the device design. If you can not get this information, I recommend to post a real photo of the device and as much information as you can; mounting, power input, etc.

200g acceleration of 800lbs is 160,000lbf or an instantaneous 80Ton. Not sure what the floor thickness is at your facility, but you are going to have a hard time not damaging the floor with a direct connection, let alone reducing transmitted vibrations. In addition to being a nuisance, vibrations can damage the building structure and items within.

A better plan than direct mounting is to mount the device to a large mass like concrete, but then have something flexible between that concrete mass and the floor. That way, when the 800lbs goes up at 200g, the 8000lbs of concrete only accelerates at 20g and that motion is absorbed by a suspension system. You would need to size it properly for the mass, but an air ride suspension system kit might be a good solution.

Remember to use vibration resistant fastening methods (welds, cotter pin bolts, etc). If the system is to operate unattended, a floor mounted vibration kill switch would be a good idea if something were to go wrong.