Vibration from the Propeller

Is the propeller clean? To open, the blades and gear need to be clean and move freely.

A 2 blade propeller will have more noise and vibration compared to a 3 blade as, for a faction of a second, the blade loading changes as the blade passes the strut or deadwood and does not have attached water flow.

Is there evidence of thrust and water flow over the rudder when initially going into gear?

A propeller out of balance will have vibration throughout the RPM curve, getting worse as the RPM is increased.  Was the propeller dynamically balanced at manufacture?  If this is a new problem look for blade damage, a “chunk” missing or a bent blade.

Old age and wear by itself does not cause vibration. If the blades are loading/unloading say at low RPM you may notice a noise but once the blades are fully open and loaded they do not cause vibration.