Tub will spin but agitator won't move on my ge washer model wpsr3090v0ww

That style of washer has a transmission tube called the "mode shifter" part#WH38X10017 It has a small electrical solenoid that is supposed to shift from the agitate to spin functions... The problem happens when the entire tub remains engaged for the agitation stroke. So you would see the entire tub moving like just the agitator would normally... That causes larger than normal waves that crest and come out the back left over flow tube. You probably need to replace the mode shifter.
Heres the manual for testing...
Appliance Repair Manual ge washer with electromechanical controls and...

and here's a link to the part:
Clutch WH38X10017

an internal clutch

My parent's Hotpoint did the same thing!! The brake on the bottom of the tub is not engaging! It needs replaced!!

what is your model number is then we can started then okay

t's supposed to be that way. If you could pull it up whenever you wanted, what would keep it from flying off during a wash cycle? The agitator is loosened from a bolt underneath the wash basket. Do not try that or you could damage the washer. Only a repairman or someone who has worked on washers should do that. Only if you had an article fall apart in the washer (a rug, feather pillow, etc.) should that area truly need cleaning. Call any GE repair shop. If this is under warranty and you have ( as shown ) the model #...........a repair inspector can fix this washer free. Have all your place of purchase documents with you. The agitator's movement back and forth is important for the cleaning of your laundry. If it doesn't function properly, your clothes won't be as clean as possible. If your agitator does not move, moves only in one direction or its movement is very weak, you will probably need to remove the agitator. Furthermore, in order to inspect the tub for leaks, the clutch assembly, the splines, or to remove the spin drum, you will have to remove the agitator.

You need to check the lid switch for continuity. A bad lid switch will prevent this machine from agitating or spinning.

Hi,
If you hear the motor go through the stages, but nothing is happening in the tub, the motor belt may be broken or off.

tub bearings may be frozen up. Can you move tub by hand?

sounds like a bad lid switch how old is it?

sounds like may be in clutch see if you can help the tub start spinning when trying in spin setting...if trying to turn or turns some and stops most likey clutch slipping