Does the shimmy happen when going straight or just when making slight turning on the freeway?
I have experienced wheel shimmy when turning at speed on the freeway and found a lower ball joint with excessive play was the cause, this was on a BMW.
Do you get any steering wheel movement when driving at slow speeds, let go of the wheel 10/15 mph and if it shakes and it does not have to be a lot, it most likely is a bad tire(s).
If you get a shimmy at a certain speed, like 55/60 mph going straight and you can accelerate through it, it most likely is a wheel balance problem.
The stock GT wheels can be sensitive to higher speed shimmy and can not really be properly balanced because you can not attach a weight to the outer most part of the wheel, no lip on the face of the wheel. Any balancer set up to attach weights to the inner part of the wheel, inside lip and center of wheel is only a compromise and calculates to what it may take to balance the wheel, this is the one thing I run into all the the time with customers is that they want their wheels balaced but do not want weights on the outside, no guarantees!
If it is only when turning at speed I would suspect excessive play in some joint in the steering linkage, lower ball joint, tie rod joint (inner or outer) and possibly the rack & pinion bearings/bushings. I have also experienced this with a faulty front shock/strut in some instances.
This is all assumptions and the only way to determine would be to actually t/s the problem. Tough when you can not look at the car!
We have a Hunter machine (CA. sorry) that can measure road force variation and I have found many new tires way out of specification, especially pirelli pilot sports (crap and noisey). I do not see many goodyear tires as to comment on, not to mention mounting and balancing tires sucks and I do not like doing it so I try to stay away from it(hide)!.
Good luck and let us know what you find.
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