I am not sure about that description of the wave with P and Q in it. I calculated the phase difference between as being 2pi/3...but for the description I wasn't sure. The question said something about P being moved with SHM...so that made me think that vertically P moves with SHM (hence I described all that) but horizontally it moved with constant velocity (as in a progressive wave).
Does this sound right or have I misread the question?