This was taken from the tech. bulletin for a Batavus, but I feel it holds true for any moped.
In the past few months, we have experienced a few rear wheels with bearing problems. We feel at this time, that the bearings, cup, spindle and cones are not the problem. When servicing or preparing a new moped, make sure that the tension of the "drive" chain is not too tight.
The drive chain should have at least 3/4" to 1" slack or play in it. Be sure to rotate rear wheel a full revolution while adjusting drive chain to assure the proper adjustment of 3/4" to 1" in all positions. If the chain is too tight, this will cause unnecessary wear to the bearings.
I'm sure tightening the chain will temporarily fix the vibration problem, but this may be an early warning sign that your rear bearing is going bad. It's easy enough to replace a bearing, but a lot harder to find a replacement wheel with a good hub that hasn't been destroyed by a neglected bad bearing. I hope this helps.
Lamborn's Miniature Engines