In figure $(A)$,mass '$2m$' is fixed on mass '$m$' which is attached to two springs of spring constant $k$. In figure $(B)$,mass '$m$' is attached to two springs of spring constant '$k$' and '$2k$'. If mass '$m$' in $(A)$ and $(B)$ are displaced by distance '$x$' horizontally and then released,then the time periods $T_{1}$ and $T_{2}$ corresponding to $(A)$ and $(B)$ respectively follow the relation.

• A
  $\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}$
• B
  $\frac{T_{1}}{T_{2}}=\sqrt{\frac{3}{2}}$
• C
  $\frac{T_{1}}{T_{2}}=\sqrt{\frac{2}{3}}$
• D
  $\frac{T_{1}}{T_{2}}=\frac{\sqrt{2}}{3}$