If two similar springs each of spring constant $K _{1}$ are joined in series, the new spring constant and time period would be changed by a factor
JEE MAIN 2021, Medium
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$\frac{1}{k_{e q}}=\frac{1}{k_{1}}+\frac{1}{k_{2}}$
$\frac{1}{k_{e q}}=\frac{1}{k}+\frac{1}{k} \Rightarrow k_{e q}=\frac{k}{2}$
$k^{\prime}=\frac{k}{2}$
$T =2 \pi \sqrt{\frac{ M }{ k }} \quad T ^{\prime}=2 \pi \sqrt{\frac{ M }{ k ^{\prime}}}$
$\Rightarrow T ^{\prime}=2 \pi \sqrt{\frac{ M }{ k }} \times \sqrt{2}$
$T^{\prime}=\sqrt{2} T$
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