Lots of possibilities, most likely of which is warped or unevenly worn front rotors. Try having them checked and ground flat if necessary. Also, worn driveshaft flex joints or bearing bushing can cause a similar problem if the steering wheel does not shake. Loose ball joints, tie rod or center link bushings will accentuate any wheel imbalance, as might worn idler arm bushings.

The steering damper replacement might help if it is badly worn, but in itself cannot eliminate the problem.

Steve

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'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7