In figure $(B),$ the effective spring constant

$\frac{1}{K}=\frac{1}{k_{1}}+\frac{1}{k_{2}}$ or $K=\frac{k_{1} k_{2}}{\left(k_{1}+k_{2}\right)}$

In figure $(C),$ the effective spring constant, $\mathrm{K}=\mathrm{k}+\mathrm{k}=2 \mathrm{k}$

In figure $(D),$ let the effective spring constant be $K$ If mass $\mathrm{m}$ be pulled down by distnace $y,$ the springs $A$ and $B$ will be stretched by $y'$ $\left(=y \cos 45^{\circ}\right)$ Total restoring force is $\mathrm{F}=-\mathrm{Ky}=\mathrm{F}_{\mathrm{A}} \cos 45^{\circ}+\mathrm{F}_{\mathrm{b}}$

$\cos 45^{\circ}=2\left(\mathrm{ky}^{\prime}\right) \cos 45^{\circ}=2 \mathrm{k}\left(\mathrm{y} \cos 45^{\circ}\right) \cos 45^{\circ}=\mathrm{ky}$

$\mathrm{K}=\mathrm{k}$ Use time period $\mathrm{T}=2 \pi \sqrt{\frac{m}{K}}$