[Not disputing your above math/calculations, but the big variable in this application is the additional mass beyond the machine, which has been already been mentioned. It is a composite of liquid, media, parts being processed, and it is conformable and is free to move. I don't see how its resonate frequency contribution can be easily assessed and factored in. For those on the sidelines, the shortcoming of using mass only in the calculations might be similar to proclaiming equal mass amounts of glass and lead have same the resonant frequency.