An autonomous mass damper is positioned proximate to each reel cutting unit in a ganged configuration of such cutting units. One mass damper is preferably mounted or directly carried on each such reel cutting unit. The mass damper is free to move independently of vertical up and down movement of the reel cutting unit as the reel cutting unit travels over the ground. The mass damper is connected to the reel cutting unit by a coupler or by coupling components that allow the mass damper to move in a counter motion to vertical up and down bouncing or bobbing of the reel cutting unit. The counter motion of the mass damper lessens or damps the bouncing or bobbing of the reel cutting unit to provide a more consistent height of cut.