Strange Vibrations

We have a 1964 Cessna 172 E with the 145hp Continental 0-300D and a
McCauley fixed pitch prop. Last Saturday, I flew the aircraft for about
an hour. We were at about 3,500 msl with an air temp of about 42F.
There were some low clouds at about 4,200 msl. No problems. Later in
the day, my plane partner took up the aircraft for his biennial flight
review. They also flew around 3,500 msl with the same air temp. A
light drizzle was now falling in places.

They noticed a strange vibration in the aircraft between about 1,700 to
2,200 rpm. They described it as a "pulsing" vibration and likened it to
the vibration/sound made in a twin when the engines are slightly out of
snyc. After the usual checks for carb ice, mixture control, etc., one
speculation was that one of the rubber motor mounts was worn and
transmitting the vibration to the frame.

Needless to say, the flight was shortened.

On Sunday, we took off the cowling and looked for anything loose,
checked the oil for anything shiny, pulled the plugs to see if we had a
fouled plug or cruddy cylinder. Other than some plugs that were showing
some wear and and one with a little lead deposit, all looked OK.

We put the plane back together and ran the engine up. Seemed OK.
Started and ran like it always did. Gagues all read like they always
do. Then, with some severe "pucker factor" we taxied out to the runway
for some very close-in touch and go's. The weather was again about 42F
with a very slight drizzle.

The aircraft powered up normally and climbed as always for two trips
around the pattern. On the third trip, my partner was able to duplicate
the vibration.

At exactly 2,350 rpm, the pulsing vibration occured and I was able to
experience it. It was about 1 cycle per second and did sound/feel like
an out of sync twin. It disappeared at 2,300 or 2,400 rpm. Other than
that, the engine ran as always.

So....any ideas? Has anyone ever experienced this concept? Is this a
mechanical problem or just an alignment of conditions that exacerbates a
principle of physics. Could this be equated to the resonant frequency
of the airplane, airframe, air and moisture conditions? It does make me
wonder since this aircraft has rarely, if ever, been operated by either
of us in any kind of visible moisture.

Thanks in advance for any comments

Al