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Hi, my name is***** burning smell was probably a pulley bearing or the alternator bearing going bad and it eventually caused the belt to overheat and come off. All of the rotating components for the belt need to be checked to see if they turn freely. Since the alternator light was on previously I suspect you will find that the alternator has failed or one of the pulleys was progressively going bad and finally came off.
Let me know if you have any questions.