I bought a Computer Dell Monitor E2020. The monitor seems to shake a lot, a simple tap, or small shake will cause it vibrates greatly. It vibrates more side to side like a pendulum when typing. I know its not the desk, since we got multiple new ones and, and tested other monitors. How can we resolve this issue? Are there any weights/material we can paste to electrical equipment to make it more stable? Holding it down, seems to alleviate the issue
It really depends on what exactly is vibrating.
If the base is not manufactured precisely and isn't sitting flat on the desk, you could get some rubber mat of some sort to pad where it sits. Of course, most monitor stands are designed with rubber feet to serve this exact purpose, so if you think it's the base rattling against the desk, check to make sure no foot has fallen off.
From your description, it sounds though like you are actually seeing physical movement of the monitor from vibrations. This can also be caused by a poorly-manufactured base, or the monitor support itself might be poorly made, such that it's not rigid enough, or has too much play in its mechanism. A good monitor stand is made from thick enough material, and if its height can be adjusted, the adjusting mechanism is designed so that the parts remain in contact at all times throughout the range of adjustment.
Are there any weights/material we can paste to electrical equipment to make it more stable?
There is a small chance that it's just an unlucky combination of the monitor's weight and position, and the monitor's own degree of rigidity and height. You could try using some mass loaded vinyl (typically sold for sound damping purposes), to change the weight of the monitor so that it doesn't resonate so easily with whatever vibration is causing the problem.
All that said, I wouldn't put too much effort into the issue. There are plenty of monitors with stands on the market that don't wiggle around at the slightest provocation. The most reliable solution is to just return these monitors and purchase ones that are better built.
If you really can't stand to give up the monitor, due to technical specs or whatever, that particular monitor (like most these days) has a VESA-compatible mounting interface, so you can just purchase a different monitor stand or mount, one that works better than the one that came with the monitor.