What do you mean moving up and down? The cover of the air box or the whole thing?
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No
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Clicked on "this" in the O.P., and watched youtube link. I'm guessing that this is not normal.
I had a similar, but not as severe, movement on the air box in the Justa. The plastic "top hats" that go thru the air box, and around the securing screws, were missing, allowing the box to move.