This sounds like interference, the CRT reacting to electrical fields of some other device like an AC fan, an air conditioner, another CRT or TV, a stereo amplifier, powered speakers, that sort of thing.
You can determine if you have this kind of interference if the frequency of the "shaking" changes with refresh rate. Shakes slower at 70 Hz, faster at 90 Hz, and faster still at 100 Hz. It should stop shaking at 120 Hz.
If you do have this kind of interference it's a beat frequency that you are seeing. The beat being the difference between the refresh rate and the power cycle of 60 Hz, for example, 10 shakes per second when refresh is at 70 hz (70 Hz - 60 Hz = 10 Hz beat frequency).
To fix this problem move the CRT away from the offending device. If that doesn't work make sure that no power cords run parallel to your video cable. They can cross each other but just don't let them run side by side.
I had an interference problem with a box fan I used to use. Put it within 4 feet of my CRT and the image shook badly (enough to make me nauseus).
I've heard of people having similar problems with some powered speakers, especially 2 channel systems where the amplifier (in one of speakers) is too close to the CRT.
However, electrical motors and florescent lights, and powerpack transformers are the biggest offenders.
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