What was found
MIA - FLT 0971 - EN ROUTE BNA/MIA, HARD UNCOMMANDED RUDDER KICK TO THE RIGHT, AIRCRAFT ROLLED LEFT AS RESULT, AUTOPILOT DISENGAGED TO RECOVER AIRCRAFT. INCIDENT ONLY OCCURRED ONCE. ALL SUBSEQUENT INDICATIONS NORMAL. FLIGHT 28,000, 300 KNOTS, SMOOTH AIR, KICK RESULTED IN APPROXIMATELY 10 DEGREE ROLL. LANDED MIA WITHOUT FURTHER INCIDENT. REPLACED UPPER AND LOWER YAW DAMPENER COUPLERS. ACCOMPLISHED ADJUSTMENT TEST OF LOWER AND UPPER RUDDER POWER UNITS. DOWNGRADED TO NOT CAT II. SYSTEM GROUND CHECKED, NORMAL OPERATION. (X)