The details of the DPDT relay are pretty much irrelevant because most of us know how the contacts are configured.
How about some detail of the motor:
The PLC switches 120V - AC or DC?
The motor is reversible - how?
What type of motor is it - PMDC, series DC, shunt DC, synchronous, universal, shaded pole, split phase, cap start, cap start & run....?
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If we learn from our mistakes,
I'm getting a great education!