Now that you've found the cause, you're only half-way there. Now the fun begins. Find out what else is loose. The rotors are a typical place for the shimmy (or worse) to start, but some worn parts may be contributing to the fun. Track bar-both ends, tie rod ends, control arm bushings-all the usual suspects. Get under it with someone sawing the steering wheel back and forth, watching and feeling all the joints. They'll all probably show at least a little play. A few slightly worn parts can add up to a badly worn part. Good luck.......