Our Patty (who is prone to being a "nervous nelly", easily startled & frightened) was really, really terrifed also. To help her get over it, we would leave the vacuum out (unplugged) near where we'd play with her. After a while she got comfortable being near it & while she was really engrossed in play with one of us, the other would turn it on for a few seconds, then a few minutes, etc so that she became desensitized to it & eventually didn't freak out anymore. She no longer reacts to it unless she is asleep & doesn't realize it's near her when we turn it on - she'll startle awake but doesn't run away or tremble anymore. Our doodle Odie just sleeps thru it all. It's important not to reinforce their fears by petting them or cuddling them when they are fearful - that gives them the signal that being afraid is good because they get extra love & attention. Just act like it's no big deal & the pup will learn from your confident leadership.
Good luck.