Amana top load washtub drum moves from side to side

Is usually a sign the washtub suspension is worn or broken.

The agitator in your Maytag Dependable Care washer uses a back-and-forth motion to move your clothes from the top of the washtub to the bottom and back to the top again. The fins on the side of the agitator help facilitate this movement. When one of the fins sustains damage or the agitator fails to move, you must remove the agitator to make the necessary repairs.Disconnect your Maytag Dependable Care washer from the electrical wall outlet. Turn off the valves supplying water to the appliance.
2 Open the washer's lid to access the agitator. Look for a 1/4-inch hex screw recessed in an opening about three-quarters down the side of the agitator.
3 Insert a 1/4-inch nut driver into the opening in the side of the agitator. Fit the nut driver over the head of the screw. Turn the screw counterclockwise to remove it.Grab the bottom of the agitator with both hands. Pull the agitator from the bottom of the washtub.

• Nut driver, 1/4-inch

The F2 fault code indicates a problem with the washer's drain system, and you must troubleshoot the problem to determine how to fix the washer and clear the code.
Clogged Drain Hose The drain hose on a Kenmore washer should remain free of obstructions so the water drains from the washtub. the drain hose behind the washer can impede the flow of water from the washer. A drain hose inserted more than 4 1/2 inches into a floor or wall standpipe drain system can cause the water to siphon back into the washtub.
Stuck Water-Level Pressure Switch Your Kenmore washer uses a water-level pressure switch in the control panel to detect the level of water inside the washtub. You can find the pressure switch behind the control panel in top-load models or attached to the inside wall of front-load models. The round switch is approximately 3 inches in diameter with a clear or black plastic tube connected to the bottom or side of the switch. The tube runs from the pressure switch to the exterior washtub. As the water fills the washtub, it changes the air pressure inside the tube and lets the switch know when the water has reached a predetermined level. A stuck contact on the pressure switch can stop the advancement of the wash cycle and keep the water from draining. A few taps on the top of the switch with a screwdriver handle can release the contact and fix the problem causing the F2 error code.

Most likely is a bad belt but could be the pump has a bad bearing in it.
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Taking a guess is all that is possible...

The drum bearings have seized.
Something has broken and jammed the drum drive pulley.
Something has become jammed between the washtub and drum.

Your next step is to remove the top of the cabinet and examine the drive, ensure the motor still spins ok and the belt is intact, pulley not broken, etc.

If you find nothing wrong the task becomes fairly major as the cabinet will probably need dismantling in order to remove the front of the washtub for a closer inspection.

there are shocks inside the machine that damper the vibration, one or more has failed, they can be replaced if you are a good do it your self er, if u have to pay to fix it replace not worth the cost of repair. the repair requires taking off all the panels to access the inside. and check cost of dampers and compare to cost versus replacement

there is a coupling between the motor and the gear box that turns the drum coupling could be broken or a missing key either way not an easy fix call a teck or a realy handy neighbour not that this will comfort you but the part is usualy cheap its the couple of hours labour to change it that hurts
Good Luck

Yes! to let you know that this is NORMAL when the washer agitates, due to the "Westinghouse" designed transmission, which in turn is called the "Franklin" design.When the agitator returns back stroke the washtub "indexes" before the agitator strokes forward. Thus moving the load around through the water while being moved back and forth.
Plus! to let you know that since the washer does NOT have "brakes" to stop the washbasket and hold the basket this design allowes the "indexing". This is one of the main reasons your washer has a safety lid interlocking device on it to lock the lid when it spins, because the washer has no brakes to stop the machine if the lid is opened during a spin cycle.

There is a large pulley directly under the washer drum that runs the transmission. There is a small one connected to the motor shaft, and a third which is attached to a spring-arm and acts as a tensioner.

Pay attention to the direction the tensioner moves. The back of the belt should go against the inside of the tensioner when it is released.

The easiest way I've found to get the belt back on is to thread it around the small pulley, and tensioner, then start it on one side of the large pulley, and rotate the large pulley to allow the belt to thread onto it.

Hope this helps.

CHECK FOR A BROKEN BELT