Out of curiousity, what would happen if a cell that was going through mitosis was injected with cyclin?

Depends on which cyclin, if it was wildtype cyclin or non-degradable cyclin, and how much. Also depends on when you inject it during mitosis!

There are thousands of papers on this topic.

Lets say you inject cyclin B at a level that is 10 times the normal amount, right at the time the nuclear envelope is breaking down.

It would speed the entry into mitosis.  Then, once the meta-anaphase transition had happened it would delay exit from mitosis.  Cells would stay in anaphase much longer: with a broken down nucleus and condensed chromosomes, and no cytokinesis.

Eventually the excess cyclin B would be degraded, and the cells would then go through anaphase.