E36 found this, is it from my 316i exhaust

Hi, I heard a knock coming from the rear while driving and thought it was the exhaust and when I looked it was hanging low. On inspection the clamp has broken on the backbox so I used wire to secure it for now.

However after my wife returned home she found a strange metal cylinder on the drive, it's solid with a bolt on one end and doesn't appear to do anything. it has a (broken) clamp on the side to secure to something roughly the same size as the mid pipe on an exhaust (pics at end of post).

There's no branding, just some random numbers. I've checked RealOEM for the exhaust diagrams but nothing that looks like this thing.

Any ideas what it is, wherwe it's from, and what it does?

Thanks.

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Looks like a vibration damper to me is the cylinder flexible on the bracket. I'd be checking the exhaust on a lift if you have rust like that.

Thanks for your response, after searching vibration damper on Google it does indeed appear to be one.

Never heard of a vibration damper before, and doesn't seem to do much, is it a BMW part attached every 316i?