Yes, if periodic = organic. Otherwise these are generic trig equations with no particular relation to "organic" motion.

Are the orbital paths of planets "organic" or just interesting physics?

To me, a truly "organic motion" would be a differential equation that describes an organic process as a function of time, like the logistic function:

http://en.wikipedia.org/wiki/Logistic_function

This has the advantage of possessing an actual relation to organic processes, rather than being a member of a large class of functions that have no specific connection to life.