Interesting. An "Osu" wouldn't come out of me uncalled for in Hajime...not the way the primal roars do
However...when in Hajime and the instructor shouts something like "Dig! Keep it going! Don't lose focus!" then a community of "Osu" would come out from everyone. I think the difference is that when we were doing hajime we would call "isshou" (together) or just kiai louder and stronger unless shouted at. The cops would call "Fighto" and "isshou" and sometimes just scream in abandon...