Whirlpool Washer spin cycle wobble

This is a typical direct-drive, top-loading Whirlpool with nothing unusual. I just got it used. The spin cycle has a pretty fierce wobble, but not quite so bad that it walks around the room. I tried it empty and it persists. I tried to look at a lot of things, and here is what I found:

[LIST]

  • I leveled it first. Didn’t help much.
  • All of the suspension springs and the counter-balance spring seem good. No rust. When I take them off, they seem to go back to their original state and each seems pretty strong.
  • The three white pads on the skate plate seem to be ok. The one in the back (which was where I thought the most noise came from) had a little extra wear on thside. But they had each only worn to a point where about 1/4 inch was apparently rubbing on metal. I traded out the back one with the left side just to see if that would help.
  • I looked under the agitator for wear near that spanner nut. Looks ok.
  • The bottom of the machine looks really clean, but I have a hunch this was a pawn shop item once upon a time (there is a faint note on the back that says not to pawn it)
  • When I stop the spin cycle, I hear liquid slosh, presumably from the ring.[/LIST]What else should I check? Should I replace the springs anyway?

Help!! I am using this washer but I don’t like its wobbling.

I was given a second one for parts… and it has a similar problem that may be easier to fix if I can check it all out. The second one spins its spin cycle like this… spin… spin… spin … WOBBLE … spin … spin … WOBBLE … spin … spin … WOBBLE and the wobbles are pretty SEVERE on it. I can watch the center of the shaft do this with the agitator off, and it stays centered until each violent wobble. Strange!