Take note if the "vibration" at the dock is happening only when the wind is exactly abeam. If this is the case it is caused by vortex shedding (as alluded to by Bosun). My mast does this in a bad way if we're side on to the wind. Usually we're at anchor or at a slip with winds that previail from bow or stern. Occasionally when we're at a guest dock (just about never) we will get the harmonic pumping. It's really profound on my boat and my triatic stay causes the mizzen to whiplash!
So how do you fix it? You can orient your boat so that you're not side on to the wind, or you can hoist or install something alongside the mast to disrupt the vortex shedding. The easiest way to do this is to hoist a fender in the rigging. (don't forget to tie a downhaul line to the fender otherwise you'll have a new perminant fixture in your rigging!) Unlike more solid objects it doesn't make noise if it bumps the mast a little and you can move it up and down until you find the spot that disrupts the harmoics. The vortex shedding will likely happen all along the mast but you only need to disrupt it in just the right spot to stop the mast from developing just the right harmonic to "pump".
I pass this information along to you in the hopes that you don't do what I did, which was re-tune my rig 20 times (and invent a few new words) before I found out what was really going on. Unlike RichH's experience, no amount of rig tuning helped my situation. Besides, my rig was tuned for sailing, not to allieviate pumping, before I messed with it. Now it's back to being tuned for it's original purpose.
Once you find the right spot with your fender, if it's convenient to do so, consider installing a radar reflector, mast steps, deck light, or whatever piece of mast gear you might want so that you'll always have a perminant piece of gear "hoisted" to disrupt vertices in the future. I prefered this option over a check-stay or baby stay, which would be one more force direction on my already overly complicatedly (sic) rigged ketch.
Vortex Shedding:Vortex shedding - Wikipedia, the free encyclopedia
PS It's really fun when your neighbors finally get the courage to ask, "Is that a FENDER in your rigging?"