For any perfectly circular motion, the centripetal force does no work every. Even in periodic motion the net work still turns out to be zero.

Consider this, the two components of the work equation is Force and Displacement, but remember that force and displacement have to be in the same or opposite direction. In perfectly circular motion they will also be perpendicular to each other, so no work.

When an object is in periodic motion, it must return to it's original position once a cycle, that means the total displacement in one cycle is zero resulting in zero work. But if the object only completes part of a cycle then work in done.