1993 Ford Mustang

Hi ericn22. Welcome to the forum. It is likely nothing more than slightly warped front brake rotors. This can happen on any car and will often even occur with new rotors. Once they are machined, they will be perfectly true, but then the old brake pads won't match exactly so just be aware that you won't have 100 percent stopping power until the pads wear to match the rotors. That could take as much as a couple of hundred miles or it could not even be noticeable.

It doesn't match you description exactly, but if you feel the same shimmying when you are not applying the brakes, suspect a sticking front caliper. That is easiest to diagnose with the front end jacked up and by trying to spin the wheels by hand. If one won't turn easily, that caliper and brake hose should be inspected further.

Caradiodoc