Imagine two blocks of masses $m_1$ and $m_2$ joined together by a spring of spring constant $K$.
Now let the spring be stretched by a distance $X$ and then the system is released. suppose during the stretching the block of mass $m_1$ moves towards left by a distance $A$ and the block of mass $m_2$ by a distance B.
Now the centre of mass of the system at any instant will remain at rest. Now let it be present at a point P in between the two blocks. so can I depict the oscillations of the two blocks as two independent oscillations about the centre of mass?