I have same Problem on My 2011 R/T , Goodyears , Had Bal. at Discount Tires and they are much better but Still very light Shimming at 60-65 MPH.
Going today to get 4 Wheel Alignment at My Shop I use, Not Dealer, Will post finding.
Just beginning to think Goodyears are Crap Or Dodge Rims Are.
Balance took 9-12 .25 Weight's on some of the Rims, That is a lot, What's up with that?
Only Problem, Love the R/T!

 

Went back to Discount Tires, Checked them again,Guess what, Two of Goodyears Fortera's
Were out of Round, Only 3,000 miles on them, Like new.
Got credit for two tires and Purchased 4 new Yokohama Parada"s.
Look's like problem solved, Nice Tires.
Balanced Goodyear's yesterday, Most took 9-12 a Tire .25 Weight's.
Today watched balance and were between 2-4 a Tire .25. Weight's
Sign that something was way wrong!
Goodyear's are a piece of Crap! Stay away from them.

 

I finally got my shimmy figured out at the dealership. Took 3 tries. Very annoying but she's smooth now.

Gonna get some better rubber when these wear out.

 

So are you going to share what it was? lol

 

Done with break in period on my '14 R/T, so I have been roaring down the highway with my Escort radar detector. No shimy or shake at all. Had the beast up to 95mph many times, smoother than my Jaguar. I was going to get aftermarket black rims with polished lip, but the ride is so smooth, I don't want to screw it up.

 

Bet it was out of round tires……..

 

Just a balance issue. They balanced then road forced them. Had to spin a tire on one of the wheels to dial it in.

It took 3 trips to the dealership because they were lazy and just trying to pump out vehicles. I took the service rep (or whatever his title is) with me on the highway and showed him the shake. Told him it was the third visit for the same problem and I demanded a rental for as long as it took to get it figured out be I wasn't taking it back until I road tested it and approved. So it took them 6 hours to figure it out. Once they were spending money on a rental. Just needed to motivate them.

I had the headliner replaced last month and they crushed the new one in some places. Pointed that out and told them that would need to be redone as well. Nice to have their attention now.

I was too nice and trusting in the beginning. I learned.

 

Just changed my tires to Continental Cross Contact 285 50 r20. No shimmy until now somewhere around the 45-65mph range after 1,100 miles. I'm trying to figure out why its starting now ? What is a road force test and how do I find out if they have it and not just bs me to take my money ? By the way Iwas just at the dealership for a bunch of little odds and ends under warranty and iI figured let me take it to where I bought it and maybe get something as a courtesy......bull**** ! They broke more **** still charged Chrysler for the workand ththat's where Iwent to another dealer to correct and fix what they charged for.....Chrysler called me to find out why I was doubling the work and when Itold them what they did with proof of the following ddealership they did not pay them for any parts or labor which came out to $2500.00.

 

You most likely slung a weight, go get them balanced again.

 

OK, so I got a different explanation for the shimmy issue. Don't know about all of you, but mine is primarily when I start out and then gets better/goes away after a few miles. I talked to the folks about road force balancing them and the guy told me he would do it but it likely wouldn't fix the problem. I'm running Nitto 420s 284/40/22, so they are not cheap tires. He says the issue is the nylon cap that they put over the belts to help keep the rubber from 'wondering' at higher speeds. This nylon is apparently pretty pliable. With the weight of this vehicle, the tires tend to flat-spot when it sits for a while as the nylon cools down. This causes a shimmy until heat builds-up in the tire a the nylon gets round again.

Now, I'm no tire guy, but a buddy of mine is and he agreed. With wider more performance oriented, low profile tires, it is even more evident. So...in the words of Top Gun (yea, I'm that old), "that may be bull ****....but it's really good bull ****..."

BTW - my winter Michellin's (285/50/20, more sidewall) have no shimmy what-so-ever (not performance oriented)...further evidence that this may in-fact be true...