What was found
WHEN CENTER TANK FUEL WAS NEARLY EMPTY, A VIBRATION WHICH IMMEDIATELY STOPPED WHEN CENTER PUMPS WERE TURNED OFF. VIBRATION NOT NOTICED UNTIL CENTER BOOST PUMP SWITCHES WERE TURNED OFF AS THE LOW PRESSURE LIGHTS BEGAN TO FLICKER. ACFT GROUNDED. TRANSFERRED FUEL TO CENTER TANK. USING LT CTR BOOST PUMP, TRANSFERRED FUEL TO WING TANKS. DUPLICATED CYCLIC VIBRATION. VIBRATION BEGAN AT THE SAME MOMENT THE LT CTR BOOST PUMP LOW PRESSURE LIGHT BEGAN TO FLICKER. TRANSFERRED FUEL BACK TO CENTER TANK & TRANSFERRED FUEL BACK TO WINGS USING RT CTR BOOST PUMP. DUPLICATED CYCLIC VIBRATION AS RT CTR BOOST PUMP LOW PRESSURE LIGHT BEGAN TO FLICKER. NO DIFFERENCE IN VIBRATION BETWEEN LT & RT PUMPS NOTED. DETERMINED TO BE NORMAL PUMP CAVITATION VIBRATION PRIOR TO AUTOMATIC OR MANUAL PUMP SHUTOFF. REPLACED RT CENTER TANK BOOST PUMP MOTOR IAW AMM 28-22-41-000-801 & -400-801. OPS AND LEAK CHECKED GOOD IAW AMM 28-22-41-710-801.