Spin basket (drum) does turn in spin cycle

Spin basket (drum) does turn in spin cycle

I have a Kenmore 400 (model #: 11029422801) and the washer goes through the wash cycle without problem until it hits the spin cycle. During the rinse cycle, it appeared that the agitator and drum spun in tandem when the water was draining. But in the spin cycle, only the agitator spun and not the drum. I've been advised that this may point to a faulty timer, but a bad clutch seems to make sense too.

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