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I was watching "Build it bigger" or something similar, about earthquake prevention in towers. The trick there, at least in skyscrapers, was ballasts partially filled with water.
So i placed a bottle of household cleaner on the top. Its not a perfect solution, it is an improvement though; I have hardly noticed the machine building any standing oscillations since. I think you could use multiple bottles, and improve the stability.
https://www.youtube.com/watch?v=Is_X-t8xW_8
Whaddya think?
Any thoughts about measuring the vibrations?