If the engine is vibrating within a certain rpm range, what is the likely cause?

3 answers

If the entire engine vibrates in a certain frequency range, then there may be a resonance between the exciting frequency which is the engine rpm/60 and one of the six natural frequencies of the engine on its mounts.
What do you mean by a "resonance"?
Oh, hummm
Well first of all google the words "Natural frequency" and "resonance".
The idea is that if something vibrates at a certain frequency it can be pushed at that frequency and the resulting motion will be large.
An example is pushing a swing. If you push it at the same frequency that it wants to swing, it moves a lot. If you push it too fast or too slow, it is more difficult to get it going.