The flex disks can be easily inspected by crawling under the car - one in front next to transmission and one in the back next to differential. I recently replaced one of mine, it was broken and when you took off fast it made a metallic noise. It was probably twisting so much it was going metal to metal with something. It did not make noise running down the road.

Center bearing is probably the noise maker - should be able to tell by inspecting, if it needs replacement. The drive shaft has to be removed to change it - at least a 4 hour job for a pro; the bearing costs about $30. If you do it yourself, make sure you mark all components with white paint, as it has to all go back together the same to maintain balance. There are posts to search on for more details. A Haynes manual has a good procedure for this job.

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1976 240D
1987 560SL
2007 E320 Bluetec
1998 C280 (now son’s car)
1982 240D Manual - Sold