The force acting on the particle will be centripetal force ( {but is not constant in it} and the gravitational force will also act as the motion is in vertical circle. The centripetal force is inversely proportional to distance of particle from origin. And in SHM the force has to be a type of which does not resemble with it. Therefore, it is not SHM and it does not oscillate about any mean position. But it has constant time period in its motion, which means it is a periodic motion.