$\begin{aligned} & \frac{1}{\mathrm{k}_{\text {eq }}}=\frac{1}{\mathrm{k}_1}+\frac{1}{\mathrm{k}_2} \\ & \frac{1}{\mathrm{k}_{\text {eq }}}=\frac{1}{\mathrm{k}}+\frac{1}{\mathrm{k}} \Rightarrow \mathrm{k}_{\text {eq }}=\frac{\mathrm{k}}{2} \\ & \mathrm{k}^{\prime}=\frac{\mathrm{k}}{2} \\ & \mathrm{~T}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{k}}} \quad \mathrm{T}^{\prime}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{k}^{\prime}}} \\ & \Rightarrow \mathrm{T}^{\prime}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{k}}} \times \sqrt{2} \\ & \mathrm{~T}^{\prime}=\sqrt{2} \mathrm{~T}\end{aligned}$