Sounds like brake pulsation. Probably from the front brake rotors. Don't cut them, chuck them and get new ones, replace the beat up pads at the same time and adjust the rears-if drum brakes in back.
Brake pads/rotors are usually to blame for vibration during heavey or normal braking
I agree,new pads, rotors, all the way around will help. But if they are bad, you might want to have the rubber lines checked for cracks to ensure future safety.
A pulsating brake pedal which is known in the automotive world as spongy brakes is caused by worn or warped rotors/drums and/or shoes/pads. To correct this problem visually inspect the parts.If the rotors are not perfectly smooth then replace them.
brake rotors out of round
Your brake rotors are warped.
your drive belt is streached or bad tension springs.
It would be the rubber pad that sits on your brake pedal. Unless they were referring to brake pads, which are the pads which enables your vehicle to stop by pressing the brake pedal.
brake switch located on the top of the brake pedal
Usually that would be caused by a faulty brake light switch connected TO the brake pedal. If the brakes work the pedal is probably ok.
Check the switch adjustment on the brake pedal arm.
Pulsation in brake pedal when stopping? yes and also a shake or shimmy in the steering wheel when brake. your brakes may also chatter
Probably warped brake rotors. They can be removed and resurfaced or replaced with new ones.
It should be on either the pedal shaft or the pedal frame.
Check the switch on the brake pedal
out of brake fluid?