Welcome to the dreaded Death Wobble (DW). I've generally found that a worn or loose part allows a bump to escalate into full-on DW. Most common is a loose or worn out front
trackbar.
Have somebody turn the steering wheel to full-lock while you watch both ends of the front
trackbar. Have your helper bounce the steering wheel back and forth off of full-lock quickly, this will reveal any play in the ends of the trackbar.
There are other causes, like loose or worn out control arm bushings, bad unit bearings, etc.