Physics - SHM Question with Solution | TestHub

The ground is frictionless (wheels), so no external horizontal force acts on m + M; the spring force is internal between them.

Both masses oscillate about the fixed centre of mass. The relative coordinate x obeys $\mu \ddot{x}=-kx$ with reduced mass $\mu =\frac{mM}{m+M}$.

$T=2\pi \sqrt{\frac{\mu }{k}}=2\pi \sqrt{\frac{mM}{k(M+m)}}$. Hence (C).