Washer agitates the drum back and forth violently, everything eles is ok

SOURCE: GE Washer Tub has sunk and is grinding on bottom

I had the same problem and as near as I can tell, we ran a load the was simply too big and the upper chasis "droooped" just enough from the weight to cause the metal to bow. As a result, the bottom of the tub assembly was rubbing against the lower metal chasis, creating a loud grinding noise. Metal filings indicated the wear point. I took a piece of wood that is about 1"x3x height and wedged it in front and slightly to the left of the motor, running straight, up and down. the board stands straight to take out the bowing- lifting the tub about 1/4" more. This was just enough to provide the clearance needed to prevent grinding. If the vertival board is too long, you won't be able to get the front cover back on.

SOURCE: GE washer model WJRE555OH1WW - agitator free-wheels.

You need a new agitator dog. Ask your appliance parts guys about it.

Pull off the softener body, remove the cap and remove the 7/16" nut and pull the agitator top off.

You might have to use some penetrating oil and a block of wood to tap the top half before it will come off.

Transmissions are pretty tough and usually don't break.

SOURCE: GE washer whdsr315 will not agitate, everything

Pull off the softener cup
pull of the cap underneath
unscrew the bolt
pull up on top of agitator...it might need persuading

SOURCE: washer agitates so vigorously water sloshes out of

sounds like to much water check diaphram switch this controls the amont of water taken in this is not normal operation also check that the drum dampers are working ok or have not come adrift, when empty if you was to push the drum back and forth you should feel quite a bit of resistance if it moves easly then i would check the dampers

SOURCE: GE Washer WWSR3090T8WW does not agitate

Sounds like a transmission failure to me?
Good Luck !