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neck bearing would be the first thing,but just because a tire is new doesn't mean its round.u can balance a brick but it will shake if u try and roll it.
If you are standing on the seat when this happens, try putting a toe on the bars or avoid the tar snakes.
Seriously, check the head bearings and make sure they are well greased and properly tightened and if the problem persists or gets worse, you may need to replace them. Lightly holding onto the bars your arms become stabilizers even if you are not conscious of the effect. Some bikes you can ride for miles on end without any noticeable change riding hands free...others not no matter what you try.
Not a wise thing to do anyhow, other than temporarily for minor tasks that require two hands.
i'd had no experience with roadglides, never even sat on one, but decided to buy a 2013 roadglide ultra a few months ago. the dealership rolled a demo 2013 RGU out for me to ride to help me make my decision. of course i let go of the handlebars like i used to do regularly on my 08 streetglide. headshake from about 20 to 40 mph. i asked them if that was common with roadglides and they told me that the roadglides require 4 lbs of pressure or weight on the handlebars. no biggie, as i don't regularly ride with both hands off the bars. so i buy the 2013, same issue. front end shake from about 20 to 40 mph. i place one or both hands on the grips, and no more shake. above 50, no shake at all with hands off the bars. i think the next time i'm at the dealership where i get work done on my bikes, i'll have them adjust my neck bearings properly.
Had the same issue with my Limited. Low speed shake and tendency to follow the snakes. Adjusted the head bearings and it all went away. On a straight, smooth road I can set the cruise and ride for a mile with hands off if I want to.
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