[Bob Putnam]

OM,

If you actually have play (moving the steering wheel more than 1" does not move the rack), I would try and reduce that first. You could have play in the rack itself or play in the steering column universal joints. Check the radial play at the ends of the rack. Most racks have preload adjustment (rack against pinion). Adding preload will add a bit of dampening too.

If the shaking problem persists after the play is fixed, have the tires balanced (and check for runout).