My '87 E30 manual did exactly that. Went away after a driveshaft rebuild.
I think the centre bearing was the culprit, but the rubber coupling
(expensive) was also replaced so that could have been a cause too.
Make sure you have it rebuilt and balanced professionally and with only
genuine parts. I had to have myne overhauled again 6 months down the line
due to a vibration at speed.
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