I started it up and took another good look at what's happening.
This only happens with the A/C compressor on.
It seems that at between 1500 and 2000 RPM, the A/C belt between the fan pulley and A/C pulley oscillates (vibrates) at about 1/2 inch up and down between the two pulleys. Between that RPM it vibrates so much that the compressor actually vibrates because of the vibration caused by the belt.
Above 2000 RPM or so, the belt smooths out without vibration, and the compressor doesn't vibrate either.
Yes, the A/C belt is tight -- actually tighter than it should be (about 1/4 inch flex).
If the A/C is not on, this does not happen -- everything smooth at all RPM's.
So why is the fan belt vibrating with the A/C clutch engaged? Is it the drag on the clutch only between 1500 and 2000 RPM that is causing a harmonic vibration and the belt vibration???
Never saw this before in my lifetime.