IMPROPERLY SECURED AIR CONDITIONING HOSE IS INGESTED INTO LEFT ENGINE OF B737-500 WHEN PARKING AT ARR GATE.

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WE PULLED INTO ZZZ WITH SAFETY ZONE CLR. AFTER THE BRAKE WAS SET WITH R ENG SHUT DOWN; THE JETWAY WAS BEING MOVED INTO POS WHEN AN ODD NOISE AND VIBRATION STARTED. I SAW THE JETWAY TOUCH THE FUSELAGE AT THE SAME TIME THE NOISE STARTED. I THOUGHT THAT THE JETWAY WAS MALFUNCTIONING; MEANING THAT MAYBE THE MOTOR WOULDN'T DISENGAGE; SO THE JETWAY WAS BOUNCING AGAINST THE AIRPLANE. I EXPRESSED MY CONCERN TO THE CAPT AND SAID THEY BETTER GET THAT THING SHUT OFF. THE CAPT SAID HE THOUGHT IT WAS JETBLAST FROM ANOTHER AIRPLANE. I DIDN'T THINK THAT WAS IT; BECAUSE THE FEELING AND NOISE WERE VERY ODD. WITHIN SECONDS; THE 'A' FLT ATTENDANT BEEPED THE DOORBELL AND THE CAPT LET HIM IN. THE FLT ATTENDANT DIDN'T HAVE ANY INFO AND WANTED TO KNOW WHAT WAS GOING ON. THEN I SAW THE JETWAY MOVING AWAY FROM THE AIRPLANE; SO I THOUGHT I MUST BE RIGHT. THE NOISE DID NOT STOP; HOWEVER. I THEN LOOKED BACK FORWARD TO SEE A MECH UP ON THE TUG; GIVING THE KILL SIGN AND POINTING TO THE L ENG. IT TOOK A FEW MOMENTS TO GET MY HEAD OFF THE JETWAY IDEA TO REALIZE WHAT THE MECH WANTED. I DON'T REMEMBER IF I THEN SAID SOMETHING OR IF THE CAPT JUST FIGURED IT OUT HIMSELF. EITHER WAY; HE SHUT DOWN THE L ENG AND STARTED THE APU. WE WERE WITHOUT NORMAL ELECTRICAL PWR UNTIL THE APU WAS ON-LINE. THE FLT ATTENDANT ASKED IF THEY SHOULD DISARM THE DOORS AND THE CAPT SAID YES. WE RAN THE SHUTDOWN CHKLIST AND THEN WENT TO THE JETWAY TO DISCOVER THAT THE EXTERNAL AIR HOSE WAS INGESTED INTO THE L ENG. APPARENTLY THE LOCK MECHANISM ON THE HOSE CRADLE EITHER WAS NOT LATCHED OR WAS BROKEN SO WHEN THE JETWAY WAS PUT IN MOTION; THE CRADLE WAS SENT ROLLING TOWARD THE ENG WHILE IT WAS STILL RUNNING IN PREPARATION FOR GATE.