since it's not a synchronous motor, the motor rpm oscillates as well
A large induction motor at no load is effectively at sync speed. In the US grid, that would mean a rock stable speed (there may be notable grid frequency variations in other places).
Also, although I placed the motor on the rubber base or the pump head, I still noticed some cycling (0.015-0.03) but not as bad without them.
That raises a question for me whether initial test (where you saw cycling from 0.07 to 0.22ips) was done in a shop or in the field.
[ul]
[li]In the field, for vertical motor mounted on top of pump I would oridinarily expect resonance to manifest itself with high directionality (big difference in resonant vibration magnitudes in the two radial directions) due to the asymmetries introduced by the cutout within the motor stool in vicinity of the packing/coupling, and by the attached piping.[/li]
[li]In the field, I wouldn't be as surprised to see a (postulated) varying stiffness over time as I would in the shop (there may be theoretical mechanisms for a pump casing to be affected by changes to the system and the attached piping, in contrast to a shop mounting configuration)[/li]
[/ul]
Based on this it would shatter the premise of natural frequency affecting the cycling or oscillating vibration.
I wouldn't pay as much attention to cycling at lower magnitudes like 0.015 ips to 0.03 ips. Those low magnitude oscillations are not as notable / significant imo, at least without a lot closer look. (btw do you know if that was still predominantly 2x.. I'm guessing it wasn't).
And sometimes things end up happening we just can't fully explain. It's a learning opportunity for everyone.