“In the groove” can mean “attuned to doing something” or “doing something easily and well.” Examples: I was uncomfortable at first, but now I'm beginning to get in the groove. Fred began to get in the groove, and things went more smoothly. I haven't played in a month, but with a few more practices I'll be right back in the groove. “In the groove”’ is usually preceded by “be” or “get.” Note that the preposition “in” is used. In the examples you use, the expression seems to be out of place. For example, I would not associate a “focused study session” with being “in the groove.” The expression implies a satisfying, relaxed situation, something smooth. A similar slang expression used by my generation, when we were young, is “groovy,” meaning, of course, “being in the groove.”

to enter into the spirit of the situation or circumstance of the moment. to get into the groove may also be a synonim for the more common expression to get into the habit of doing something or you can clear your doubt from this forum http://forum.wordreference.com/showthread.php?t=197383