If two similar springs each of spring constant K _ 1 are joined in...

$\dfrac{1}{{k}_{eq}} = \dfrac{1}{{k}_{1}} + \dfrac{1}{{k}_{2}}$

$\dfrac{1}{{k}_{eq}} = \dfrac{1}{k} + \dfrac{1}{k} ⇒ {k}_{eq} = \dfrac{k}{2}$

${k}^{'} = \dfrac{k}{2}$

$T = 2\pi\sqrt{\dfrac{M}{k}}$

${T}^{'} = 2\pi\sqrt{\dfrac{M}{{k}^{'}}}$

$⇒ {T}^{'} = 2\pi\sqrt{\dfrac{M}{k}} \times \sqrt{2}$

${T}^{'} = \sqrt{2}T$