I've been working with DaVinci Resolve 12 for less than a day, and I have no idea how to solve these problems using solutions that I'd use in other NLEs.
I shot some good looking martial arts footage at the rates of 23.976 FPS at 1080p and 59.94 FPS at 720p. My project settings are at 1080p, 23.976, and playback is also at 23.976.
I added some of of the clips at both framerates to the media pool and the behaved just fine. The 23.976 clips play at normal speed, while the 59.94 clips play in slow motion just as intended. (Take note: the metadata also lists the clip at 59.94.)
Now we move on to the timeline. Here's where everything goes wrong. The same clips are listed as 23.976, and they play in real time, not slow motion.
And if I try to play at 40% speed, it comes choppy out like I'm stretching a 23.976 clip, not a 59.94 clip.
Use Clip Attributes to change the speed of the clip to 23.976fps. Don't change the speed in the edit page per se. Be aware that once you change the clip speed, this will change the edit since the clip will now be X% longer than it was before.