First of all it shouldn't start running as soon as you plug it in. Either the switch is already ON or there is something wrong with the switch and if there is, that can be electrically dangerous, so check it out. The switch should be controlling the electricity.
Shaking while running is either some rotating part out of balance or flat spot(s) on rubber rollers or on the belt(s). Sometimes such flat spots can be smoothed out by just running them for a while (hours) but don't count on it; better to replace with fresh rubber. Could be a loose setscrew on one of the pulleys. And if the shaking is very violent, it might cause other damage, so look for and fix the problem. It probably is not terminal though it may be more hassle than you want to go through.