I'm having trouble imagining the sound you are hearing.

You say it's coming from the middle or the rear of the car?

Maybe the sound is a bad flex disk.

A hesitation could be a sign of a bad engine wiring harness, but you'd likely have a check engine light, though. Bad coil wire boots are a more common cause of a hesitation, though.

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Paul S.

2001 E430, Bourdeaux Red, Oyster interior.
79,200 miles.

1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".