Shaking or trembling of a computer screen is often caused by interference from another device that is within a couple feet. It can also be caused by another monitor close by. If the removal of these objects does not stop the trembling, the monitor may have built up magnetism and need to be degaussed.
Find the menu button for your monitor. This is usually on the front of the monitor. It is sometimes on the side of the monitor.
Push the menu button. Scroll down until you find the screen option. Select "Screen."
Scroll down to the degauss option. Select "Degauss." Select "OK." The screen will make a tuning sound, as if you hit a guitar string. The screen will shake and vibrate. The shaking should now be gone. If it is not, it will need to be looked at by a professional.