Would be interesting to see what frame rate (fps) the K2 records in using each setting, 60hz and 50hz...
To verify the actual frame rate used when you choose the 60hz option or 50hz option, on a windows PC (not sure how to do it on MAC) download a video from the K2, right click on the video file and look at "properties", select "details" to see what frame rate it was recorded in. should work on TS files...
If you try this please post the frequency and the frame rate...

The rat does not change when set to be 50hz or 60hz.
1080p 30fps, means frames per second. 30 frames pictures captured per seconds.
https://en.wikipedia.org/wiki/Frame_rate
Then what is the function of the 60hz and 50hz setting and how does it accomplish the assigned task....
the 50/60Hz function is typically for anti-flicker, and should be set to your country's power frequency. See this map: http://stjarnhimlen.se/tv/LineFreqMap.gif
Video is 720p @ 60 frames per second, or 1080p @ 30 frames per second. However, the 720p setting uses frame doubling, so it's only recording 30 unique frames and copying them for 60fps. Since the 720p/60 setting does not actually store 60 unique frames per second, this setting is not useful.
Leave the camera set to 1080p and set the frequency as needed.
I wonder why they bothered to even offer the frame rate if it's not true 60 FPS?