...I have graphed this in MATLAB, and graphically found a period of about 2.1. I am trying to apply what you suggested, but can't figure out how to calculate the period of 2.1...
The sum of two periodic functions will be periodic it the two periods are commensurable. That means the ratio of their periods is a rational number. And in that case, the period is the least common multiple of the individual periods. For non-integers p and q, the LCM is the least number z such that ap = z and bq = z for a and b integers.