Could be a few reasons but most likely a vacuum leak or the power brake booster
is defective... that is to say if you keep the car serviced... if not then it could be anything!!!!!!!!!!!!!!!
It could need a tune up, sparkplugs, distributor cap, rotor, and sparkplug wires. If it's old enough (1980) it could need a set of points !
You may have warped brake rotors. Eclipse's have a problem with that. Do you feel it in the brake pedal? You mite need a tune up If you are at a complete stop when you feel it you probably have a bad motor or tranny mount. If you are moving and you feel it when you hit the brakes it is probably warped rotors.
IT COULD BE A WORN ENGINE MOUNT. TO BE SURE, PUT YOU CAR IN GEAR PRESS THE BRAKE APPLY THE E-BRAKE AND ACCELERATE THE CAR IF YOU FEEL THE SAME SHAKING IS YOUR ENGINE MOUNTS. (BE Careful)
I'm pretty sure that ants would feel a shake when you walk by. Think about it. If an elephant walked by, you would feel the ground shake.
Sounds like your brake rotor are warped, a brake shop should be able to turn then (smooth them out) for you if there not too bad. do you feel a little shake at during normal breaking? if so then that could be the problem, but because your were going down hill it take more force to slow down so you feel it more.
you must have air in the system try bleeding all the brakes
It's difficult to get a feel for what you mean when you say your engine shakes. Do you mean a regular shake? If that's the case it might be a bad valve, sparkplug, plug wire or injector. If you mean that the engine moves quite a distance when you put it in reverse, but then comes back, it could be a motor mount. Please feel free to send an e-mail directly if you want to discuss the situation further.
easiest way to test vacuum pump is , with engine off, pump brake pedal until pedal goes hard keep pressure on brake pedal and start engine if vacuum pump is good, you will feel the brake pedal go softer so you don't have to use as much effort for pedal to be depressed
It can BE HURT BY DOING THE HARLEM SHAKE
Air in the brake lines
The power brake booster is failing.
If you mean when you are coming to a stop, and press on the brakes, you feel a vibration- this most likely means that your brake rotors are warped and need to be turned. If you mean you are already at a full stop, in idle, and you press the brake and feel a vibration- it may mean a vacuum problem in the engine or something like that. So it depends- is it your brakes vibrating, you feel it in the pedal? Or is it your engine suddenly running rough and the whole front end of the car shakes?
Well, you have to shake it for a while and when you feel its about to come out, then it will be easy to shake it out. Don't worry, it won't hurt.