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I'll try and keep it short. Last truck I had was a Silverado, it had a very slight like the tires weren't balanced and as if they would cycle together and you would notice and then go away. Not enough to really see, but when you are driving on the hwy at a steady speed you can start to feel it in your head and face. It just starts to wear on you and when you get out you feel a little fuzzy or something. Anyway, I am noticing same this on my PowerStroke. Same Cooper STT 35x12.5-17 tires but brand new. I replaced the axles on the Silverado and the shocks and it was still there. Never figured it out before I sold it. SO.. Has anyone else seen anything like this from the Cooper STT's??
When I had vibrations come from my tires it was because I had two tires snap there belts within 500 miles of each other with less then 50% of the tred left on them (285 Bridgestone Dualer A/T Revos)
I had a slight vibration in mine that you could only feel at highway speeds and it turned out to be a u-joint. Might want to take your drive shaft out and see if you have any u-joints that don't move like they are supposed to.
Before you dive into your wallet too deeply, make sure your tire pressures are correct and that they are balanced well. I've had tire vibration that was solved by re-balancing the tires. It could easily be something more involved and expensive but I recommend trying the low road first in case you can solve it easily.
My vibration turned out to be a nasty tread separation. Couldn't see it standing still and looking at the tire (rt front), but at 70mph on the freeway, it let me know. took out the fender as well. Nasty !