Wheels are likely out of balance
Steering wheel shakes
Probably a wheel balance problem or possibly a bent rim.
Tires out of balance, bent wheel, tire defect, or suspension or steering parts worn.
Warped rotors
allignment
could be bad alignment
Tire out of balance or bent wheel.
1 of 2 things or both, alignment or balance.
I have seen this with bad or unbalanced tires.
If 4x4, replace steering dampner that is a bandaid, is not addressing the real problem. could be worn or bent steering parts, bad ujoints, out of alignment or bent or unbalenced wheel.
It could be wheel balance or worn out steering joints. Have it checked by a trusted garage soon!
Could be that the steering wheel rubber bushing is worn or lose. This bushing is located in the engine compartment, between the end of the steering wheel coulomb and the steering wheel likage...Tom