[Signman]

Check your steering completely!
Had violent steering wheel shake out of the blue one weekend at Atco a few years ago.
After it left and picked the wheels up steering wheel started shaking and got worse until I stopped the car on the track. Went back to the pits checked what I could tried again same thing.
Tie rod ends and steering box were tight did the standard check on the ball joints for vertical movement but on further inspection there was ball joint movement front to rear.
Replaced the ball joints and added the damper from Pete Z for safety in the future. Pete mentioned tightening the large nut on the bottom of the idler arm if OEM will act like a damper.