Are we there yet??
I may have one on the resonator (never looked) but this is on the exhaust (muffler). I have a 328 exhaust sitting in my garage that does not have one.325/330's also have them on their second (last) resonator.
It's a harmonic damper designed to absorb/offset resonance vibration on the actual muffler at a certain frequency to reduce interior vibration/resonance(60hz on the 325, I'm not sure what it is on the 330).
I have a 328, mine has this so I don't know why you don't currently have one?
Has to be on more then automatics, the ZHP is only manual from what I am aware of, well at least this one was.i looked it up. it's the vibration dampener that "bmw loe" said before. it's on automatic models. link