Vehicle pulsation when braking

'96 Nissan Sentra GXE: car pulsates back and forth when braking. The pedal does not pulsate, the car does. The rear brakes have been cleaned and lubed and it still rocks-not a lot but just enough to notice. The mechanic said he didn’t understand why it still does that after the work. Is this dangerous? Any suggestions?

Does it move left of right or braking and less braking?

How fast (cycles per second) Do the cycles speed up with the speed of the car?

Assuming the cycles speed up with the speed of the car I would look first of a warped rotor or two. At least check each rotor.

Car rocks front to back slowly when braking at slow speed and faster when braking at higher speed.

Try one or two hard stops from 60 or so, not to lockup but just shy of that. It clears that up so many times.

Cleaning and lubing brakes is a pretty hokey thing to say.

Take the car out on a smooth deserted stretch of road and run it up to about 50 MPH.
Slowly apply the handbrake to bring the car to a stop. Do NOT touch the footbrake.
Note if the problem disappears. If it does the problem is in the front, and depending on the mileage, could be any number of things causing it.
Warped rotors, loose wheel bearing, worn suspension part, and in some cases, even a bad tire can do it.

If the problem is still there when using the handbrake then the problem is more than likely distorted rear brake drums.