Truck shakes when driving over thirty mph

Does the shaking start gradually and get worse as you speed up or is everything smooth and it suddenly starts to shake? What happens if you step on the brakes while it is shaking? Do you feel the shaking more in the steering wheel or the seat? Any noises before during or after the shaking? Does it get worse if you turn while it is shaking?

There are multiple items that can cause shaking. Out of balance or damaged tires being a large one. Next would be binding or worn U-Joints. Worn suspension bushings or shocks. Answers to the above will help narrow it down some.

A "little wobble" is not fine. That describes a tire with a broken belt.

The shaking you are describing is Ford's famous "wobble". If that started occurring suddenly, suspect a worn steering stabilizer. That looks just like a shock absorber but it pulls apart and pushes together with the same resistance both ways. It mounts between the steering linkage and the front cross member. You can add a steering stabilizer too.

Excessive "caster" will also lead to the death wobble, but changing that during an alignment is real involved. Caster is the alignment angle responsible for the steering system wanting to come back to center when you let go of the steering wheel after turning a corner. When caster is adjusted too high, the steering comes back so fast that it overshoots and goes the other way. Road forces on the tires keep that going until you slow down.

If braking at higher speeds makes the wobble stop, suspect a broken tire belt along with a deteriorated control arm bushing and/or sloppy tie rod ends. A wobble has to be caused by something that is rotating, but sloppy ball joints, tie rod ends, and bushings will happily allow a broken tire belt to move things around that hold that wheel in position. All of those things are connected to the spindle which is connected to the steering linkage and steering wheel.

A sticking brake caliper can also cause shaking in the steering wheel. Once that starts to occur, you can identify it by stopping on a slight incline, then shifting to neutral. The truck should creep down hill on its own when you release the brakes. If it does not, you will also find one wheel is much too hot after a drive at highway speed.