Agitator wobbling from the stem. it comes right

First, a huge thanks for including a video of your problem. I wish all answer seekers would do the same. It helps greatly.

The video helps greatly, but is missing many important parts/areas to help fully diagnose. One thing that I noticed, tho it was a "split second" shot, was the wobble in the agitator, which seemed to wobble/vibrate in greater magnitude than the tub. The agitator should sit firmly on the shaft, and not wobble so much. (if a 2 piece agitator, the smaller finned top section is normal to wobble a little bit more tho).

The roaring noise indicates another problem, most likely a worn tub bearing. I'll include a link to a YouTube video that shows replacement of a tub bearing. Also make sure the 4 short upper rubber "shock-dampening straps" (tubular in shape) are not overstretched or broken from age/use. If so, they need replacement.

The general movement of the tub and motor assembly in your video is within the realm of "normal". But is perhaps on the upper limit of normal movement.

Tub Bearing Replacement part WH2X1198 GE Washer Repair

It sound like you have a Moen Posi-temp faucet and the handle is broken. It is probably an acrylic hdle with a tear drop shaped cover. Take a knife and slide it under the cover to pry it off. Unscrew the center screw and the handle will pull right off. You will see two shoulders inside the hdle, one of which will be cracked and broken. Replace the hndle which can be purchased at any Lowes or Home Depot. Plumbing supplies also carry replacements, but you can probably get one cheaper at HD or Lowes.. Make sure to use the washer provided. It has two flats on the inside of washer. Slide this over the brass stem on your cartridge, NOT on the hdle screw. Install it with the flats of the cartridge in horiz. position. Try faucet. If the water comes out in the opposite temp you expect, warm is cold, and cold is warm, remove the hdle, spin the stem 180 degrees and reinstall hdle.Good luck!

On that model I believe you remove the cup on the top of the agitator and then the bolt that holds the agitator to the stem. Here is a diagram of the assembly.

OPen the center stem and then reach in and remove the next cover there should be 3 tear shaped rubber thingies that control the agitator moving in agitation mode. Change those if they show wear

you can call your parts store and tell them you need the cam kit the one with the yellow piece in it and they will know what you're talking about,the dogs are worn,if the yellow piece is in good shape you can reuse it and buy 4 dogs,those are the tear drop looking pieces and there are 4 of them,this is what is worn down,also the model number is at the bottom of the top lid,open the lid,follow the lid to the bottom and look under it and you'll see the model number on the back wall of the machine right under the lid,let me know if you see it and how you make out

you will need a flat blade screwdriver long plyers 7/16 socket and ratchet, the verry top of the agitator prys off look verry close you will see a spot to put the screwdriver, then take the plyers and carfully reach in side and pull on handle of the domed shaped piece gently. then remove the 7/16/ nut. then lift off the corkscrew top portion of the agitator. you will see 4 tear drop shaped pieces called dogs part # 80040, look at the way there in there so they can be put back right later, use a camera take pictures as you go to each step for reasembly.the thrust washer will probly need replacing to, it's the plastic washer that the cork screw part sits on. when you go to put it back together use some vasaline where the dogs go in the holder, this will help hold them in place durring assembly. look close at holder for square holes they need to line up with the flat pins on top of lower portion of agitator. use an exstention and a large socket to hold dog holder in top in agitator top wile puting it on lower half. use the bag the dogs came it to hold the bolt in the socket til you get it started, then pull bag off before tightening. use two exstentions to put inner cover back in then put main cover on you are done,be pacient this may test your pacients.

could be a bad cam. take off the button on top of the agitator. there should be a cam assembly underneath. they are just little plastic tear drop shaped objects that wear out quickly and need to be replaced occasionally.

drive coupler motor to transmission look on the floor under the washer for tear drop shaped pieces of plastic

Sounds like you need a set of dogs...(dog agits)...

Pop the top off the agitator and remove the bolt. Pull the agitator top off and inspect the dogs...(small tear drop shaped pieces of nylon)...

Sounds like the dogs lost their bite aka teeth.

Chris your agitator problem is repairable. remove the fab softener cup and the cap on the agitator down inside the opening you should see 4 pieces that look lik a tear drop is my best description for them your are wore out and do not engage when the agitator agitates replace them and you'll be good as new.