Air time/displacement calculator for floor vibration

[wakadarc]

This question might be out of the scope of this forum but,

Assume an object (lets say cube) rests on an even floor that at all points is vibrating vertically at the same frequency at all times. (a platform going up and down)

The floor is vibrating vertically at a FIXED displacement.

How can i determine the frequency in which the cube will begin to lift off the vibrating floor? (be in the air at an instantaneous point) Furthermore, can I determine the frequency that will give me X distance off the platform at time T?

 

[mfb]

Calculate the maximal acceleration of the floor. If it exceeds the gravitational acceleration, the cube might lift off (if there is a way air can get under it). It lifts off at the time the downwards acceleration exeeds the gravitational acceleration, then follows a free fall trajectory until it hits the floor again. Afterwards things can get more complicated.

 

[wakadarc]

So pretty much the acceleration of the platform needs to be greater than 1g at least for the box to have air time. I guess I can just over spec it so that the cube will jump 15mm into the air.