THE PILOT STATED THAT THE LANDING WAS NORMAL, BUT THAT A 'VOILENT NOSE WHEEL SHIMMY' OCCURRED AS THE AIRPLANE SLOWED. HE SAID, '[THE AIRPLANE] VEERED SHARPLY TO THE LEFT, [AND] UPENDED.' THE FAA INSPECTORS FOUND THE NOSEWHEEL SHIMMY DAMPENER LOOSE. THE PILOT HAD A TOTAL FLIGHT TIME OF 37 HOURS IN THIS MAKE AND MODEL OF AIRPLANE.