I would think those vibratory units would operate near their “resonant frequency” to shake more.

In a simple system the resonant frequency is the square root of K divided by M
K= the spring rate
M = mass of the tub, media, parts, liquid

Birtley Engineering centrifuges work on a similar principle to discharge the dried product without gears.

This same principle made the “Galloping Gertie” bridge collapse at a particular wind speed.
When you see STOP signs wiggling right-left right left in hurricane winds it is the same principle.