Check out the carbon brushes in the motor. Theyre graphite blocks which transfer mains power to the copper segments of the motor - located at the other end of the motor from the drive pulley. Theyre probably worn down. They're quite cheap parts and easy to replace - the holders are plastic or bakelite and are generally held in with screws or plastic clips. Also, look at the copper segments they run on to check for burning or pitting. If the segments are burnt or damaged you need a replacement motor or a replacement armature (motor part) if you can source one. Occasionally may be a fault in the motor drive circuit board - in which case replacement of board only real option.
Spin problems may also be caused if the machine reckons the load is out of balance, rearrange the load. If problem persists could possibly be a fault in the out of balance detector switch or the suspension and damping system.
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