My 2003 VW Golf has an engine rattle/vibration at exactly 3700 RPM, not lower or higher. I changed the motor mount and the spark plugs and wires, but it only seems marginally better.
Could be a loose heat shield on the exhaust system. These often rattle only at one specific engine speed.
I had the exhaust system checked out. This is more of an engine vibration - you really feel it, not just hear it.
Any other thoughts?