I have a 1998 Chevrolet Cavalier. Front end

the front brake disc is waving , out of end play ,,change front disc and you solve the problem
hope it helps

If steering wheel shakes bad tire on front. If whole car shakes bad tire on rear. Or tires could be out of balance. If steering wheel shakes when brakes applied, front rotors are warped.

this sounds like you have a problem with the brakes on that side.possibly a siezed caliper on the front or a problem with the system on the right side not moving an applying the brakes.these are the common problems.

sounds like your front end is out of alignment check your tires for wear other than in the middle and take to tire shop to see if the tires are balanced right

IF IT IS SPEED RELATED OR CHANGES WHEN YOU TURN SIDE TO SIDE AT HIGHWAY SPEEDS THAN YOU HAVE A BAD WHEEL BEARING

will try to help. when front wheels shake while applying brakes and you can feel shake in steering wheel, front brakes and rotors need replacement.rotors are warped,if you replace front brake pads, it will return[shaking when you apply brakes] suggest that you replace front rotors[both] replace [both]front brake pads. cost? i would charge [brake pads cost $55.00] labor,$60.00] total $115.00 thank you for choosing fixya.com

Check for unusal wear on the new rotor,skips/hard spots/uneven wear. If you find any of those things it would either be the new roter is out round,or you have a brake caliper piston sticking on that side of the car. You may bleed that side of the car to remove any air trapped in the system. Doing so will remove any air trapped behind the piston. Jack up that side of car and block the wheels to keep it from moving. Remove the tire and have some one to step on brake pedal while you are watching the piston, this will cause the piston to expand. Have the second person to take there foot off the pedal and the piston should retract. If all of this checks out to be ok, then turn the rotor slowly to see if it has a high/low place on it. If so then the rotor will have to be turned with a brake lathe to even both sides of rotor. If you just purchased these rotors then take the bad rotor back to the store and exchange for a new rotor. hope this will help you.

A few possibilities
1. Front disc's may be warped
2. Rear drums may be out of shape
Easy way to check gently pull the handbrake lever when going forward if the drums are out of shape you will feel vibration through the lever.
3. Front wheel bearings may have excessive play
4. Suspension component(s) worn
wishbone bushes are a common failiure on Escort's
Hope this helps
Best wishes

check the brake dust shield beind the rotor. That might be a good start. Not sure what you mean by clunking but also check your engine mounts bushing and sway bar bushing. Good luck

Anti-lock brakes mean the car shakes when the brake is applied. Try pumping the brakes.