A particle is initially at the centre and going towards the left. Let $ T $ be the time period of the SHM it is undergoing. What will be its position and velocity at time $ 3T/4 $, if it starts from the centre at $ t = 0 $? 
The center of mass of a body or system of a particle is defined as a point where the whole of the mass of the body or all the masses of a set of particles appeared to be concentrated.
The formula for the Centre of Mass:

The imaginary point through which on an object or a system, the force of Gravity is acted upon is known as the Centre of Gravity of that system. Usually, it is assumed while doing mechanical problems that the gravitational field is uniform which means that the Centre of Gravity and the Centre of Mass is at the same position.