The time period of mass suspended from a spring is T . If the...

Let $K=$ force constant of spring and $K^{\prime}=$ force constant of each part then \begin{gathered}\frac{1}{K}=\frac{4}{K^{\prime}}\\ \Rightarrow \quad K^{\prime}=4 K \\ \therefore \text{ Time period }=2 \pi \sqrt{\frac{m}{4 K}}\\ =\frac{1}{2} \times2 \pi \sqrt{\frac{m}{4 K}}=\frac{T}{2} \end{gathered}