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My 2005 SE Fat Boy is rock solid, no sign of any wobble.
The first thing to usually check is your spokes, but you don't have spokes. The next would be the tire. I rate that as a prime suspect, if it only happens at a certain speed.
Let us know what it took to fix it.
Tom
I had the same wobble until I read my service manual and FOLLOWED the instructions for steering head adjustment.
I lifted the front-end, set up the masking tape for flop-over measurement, loosened the set-screw on the fork clamp, and then gave a tap or two with a rubber mallet on top of the steering head bolt.
As it turned out, my steering head was way too loose. After tightening-up, rechecking the "flop", i buttoned everything back up. On my first ride after the adjustment, there was an instant success with no more wobble.
Best of luck getting things figured-out if you already went through of of this.
Most are saying they get the wobble on decel, but if you use the star wheel to set your throttle at 38-45mph you'll see it wobbles with the throttle trailed (steady throttle).
I'm amazed at the quality problems on these expensive bikes.
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