03 f350 28mph shimmy

[zachyfarms]

03 f350 6.0 84k i have check front end and front end seems nice and tight no bearing issues that i can tell. may have a little slack in steering box causing wander on the freeway. Either way starting from a stop have a shimmy/vibration/ you can see the dash and steering whell bouncing at apporx: 28mph +/- 1mph. on hard accel you dont notice too much as you pass the 28mph but on slow normal accel man you can feel the bounce. Drives well tires are balanced and smooth on freeway. tires have worn a little uneven.
any ideas would be great.

[96STROKER350]

You said the tires are balanced and drive smooth on the highway. Have you actually had them checked? I had the exact same problem. I took mine to the local tire shop and one was really out of balance and the other had a "ball" but I didnt notice a thing at highway speeds. But it sounds like you really do have a bad tire. Just my opinion