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 time period $$T_1$$ and $$T_2$$ corresponding to (A) and (B) respectively follow the relation.

A

$$\dfrac{T_1}{T_2} = \dfrac{3}{\sqrt{2}}$$

B

$$\dfrac{T_1}{T_2} = \sqrt{\dfrac{3}{2}}$$

C

$$\dfrac{T_1}{T_2} = \sqrt{\dfrac{2}{3}}$$

D

$$\dfrac{T_1}{T_2} = \dfrac{\sqrt{2}}{3}$$