Brakes Sound Like Bed Springs
Brake pads always make squealing or screeching noise that sounds like the friction of the chalk on the board.
Brakes sound like bed springs. When metal scrapes against metal or rubber it causes friction and has squeaking as a nasty byproduct. The squeak may go away when that particular flake wears away but usually there is another metal flake right behind it. If you are hearing a spring sound outside the passenger compartement you may have a sticky parking brake.
This sound means the wear indicator is dragging into the rotor or that the braking pads are made from a low-quality mixture and there is a metal flake in the brake. If that rubber piece fell out the spring might make noise. Look for very shiny metal scrape marks on brake rotor edges.
Also bushings like control arm or sway bar bushings can make noise with age. It will have no effect on the cars braking system. If the brakes make a springy noise then its probably the brake pedal or joints leading to the master cylinder.
Most of the time the spring can be moved slightly or lubricated to repair this. When I release slowly from the brake pedal while stopping at low speeds it makes the spring-kind noise from the pedal. A certified technician can inspect suspension to find which component is causing the noise.
They may have to be replaced also. When the pad wears down enough the plate contacts the steel rotor and makes a squealing noise notifying. Sounds like a squeaky mattress bed spring.
But if you have not cahnged the shocks sinse new I think it might be a good idea now. The dealership thought the noise was from brake switch but even after replacing that the noise is still there. Rubber hardens and cracks with age.

