Swaison's Thrush (a fleet of small sized birds of an oscine family), while migrating fly far east across North America before turning south via Florida to reach northern South America. If they do this journey every year taking exactly the same time, to and fro on the same route with the same velocity profile then under which category can we put their motion.
You know that a motion that repeats itself in equal intervals of time is called periodic, right? Let's discuss what it means exactly. It means that after some specific interval of time T the position of the body from the reference point and its velocity are the same. So no matter what reference point you choose in the path, after time T the motion "repeats” itself. Well! Oscillatory motion is to and fro motion which may be periodic or not but the important thing about oscillatory motion is that it happens about a point of stable equilibrium where a restoring force exists. In the case mentioned in the problem there is no restoring force. However the motion repeats after equal intervals. So the motion is periodic but not Oscillatory!