Saga said: "if I take my hands of the wheel, it oscillates back and forth."
Dunno why I didn't think of it before... but my 1200 does that, too...
Okay, so step back a couple'a feet here and think about this. Dan was spot-on about damper cartridges in the struts, the Saturn's suspension is very similar. Regardless of WHAT type of system (electronic, hydraulic, mechanical) Oscillation is about feedback, amplification, and phase shift. Damping, in EVERY system, reduces the amplification, extends the feedback, and restricts the oscillation.
If it has NO feeling of oscillation when your hands are on the wheel, then a tire out-of-round is not the problem. I suggested a lateral runout of the tire tread or wheel, because I experienced that problem with a brand new set of tires on my Ford pickup truck uh... three-and-a-half decades ago. Replacing one bad (brand new) tire solved it, and the lateral runout on both the rim and sidewall were invisible, but the skew in the tread was pretty obvious... over 0.250" on a dial indicator... and the tire place fought me right and left about it, I had to bring it to the manufacturer's regional office to get it replaced... I had to prove it, by putting the spare on in it's place, then moving that bad tire to the other side, moving the spare there... (PITA!)
The dynamics of a motorcycle wobble is much same as what you deal with in a car- they have caster (head tube angle, axle centerline offset, etc) to promote stability, except cars (having ackerman steering) camber in order to attain a proper rolling arc in turns. There's a certain amount of damping that occurs from the tread 'scrubbing' when in a straight line, so what we see in a motorcycle exists, but is not apparent, in automobiles.
I'm certain you've thoroughly checked it for looseness everywhere... it very well may be that slop that occurs with suspension loaded... doesn't occur with it jacked up. It ALSO may be... particularly if the car has power-assist rack-and-pinion, that there's enough slop in the rack, that the hydraulic assist servo is oscillating, and causing what you're feeling. ONE way to verify this, is to disconnect the power steering pump belt, and take it for a drive, see if it still oscillates.
I don't think the sway bar links are the culprit, but they do suck to work with, always rust and seize, I had to cut 'em off my wife's car with air cutoff tool and (mostly worn out... which is good, because it was a tight fit) disc, but fortunately, they're cheap and easy to install.
And after all that, it struck me...
Do you drive without your hands on the wheel often? (Two-handed tea drinking, with pinky finger extended) :smilie_happy: :smilie_happy: :smilie_happy:
(British answer: Only when I'm in the LEFT LANE... )