What was found
A LOUD 'BANG' WAS HEARD ON INITIAL GEAR RETRACTION AFTER TAKEOFF. NOSE LANDING GEAR UNSAFE LIGHT ILLUMINATED AND VIBRATION WAS EXPERIENCED. FLIGHT RETURNED TO DTW AND SUCCESSFUL OVERWEIGHT LANDING WAS ACCOMPLISHED. PERFORMED OVERWEIGHT LANDING INSPECTION PER MM 05-51-00, CODE 10. REPLACED DAMAGED LEFT FORWARD NOSE GEAR DOOR, DOOR STOP CABLE, AND FORWARD DOOR RETRACT LINK. OPERATIONAL CHECK OK ON GEAR SWING. AIRCRAFT RETURNED TO SERVICE.