The most common cause of this problem is warped brake rotors. Get it replaced soon. Whenever you replace rotors, you should replace the pads. The old pads will have conformed to the shape of the rotors, so braking efficiency and life will be down if you use them with the new rotors.
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Warped brake rotors........
Normally this is caused by warped brake rotors.
Vibration when applying brakes is most likely warped rotors. Another cause could be loose caliper bolts.
If when applying the brakes ,roorts. If when driving only a bad tire.
The brake rotors are warped. Machining or replacement of rotors necessary to correct that.
Most likely it's caused by warped brake rotors. Heat and time gets them all eventually.
If the rotors are warped it can cause a shake when you hit the brakes.
If the steering wheel shakes, but to car doesn't, when applying brakes - your front rotors are warped (if you have disc brakes)...if you have drum brakes, the drum could be cracked or the pads worn unevenly If the whole car shakes, and the steering wheel only seems to react to that, when applying brakes - see above statement, but apply to the rear end. If the whole car shakes, including the steering wheel - all four corners are bad, and you're an accident looking for a place to happen soon. In any case, go to your nearest service center ASAP.
The brakes are unevenly calibrated. The brake on one side is applying first, and with more power than the other side.
Good question. You may have an antilock brake circuit that is not sensing the brakes correctly and improperly correcting. Anti lock pulses the brakes when you apply them. I don't know if this is perfected or not.
Try having your tires balanced and rotated. I used to have a car that would shake very bad when applying the brakes and I did everything you did. Then a guy told me to have my tires balanced and rotated and it fixed it until the tires became unbalanced again.