I think "getting into the groove" is a more recent expression, from record players, when the needle would be "in the groove" and the music was playing and everything was, well, groovy.
Dunno about "in a rut" I think it's gotta do with farming.
A rut is, specifically, a track caused by a wheel or "habitual passage", or a groove in which something runs. Ruts built specifically to ease transport are called "wagonways" and are the origin of modern railways.
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Dunno about "in a rut" I think it's gotta do with farming.
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