b
(b)

The first two springs are in parallel.

So, \(k_{ eq }\) of \(1^{\text {st }} 2\) will be \(=2 k\)

Then it becomes

The springs \(2 k\) and \(k\) are in series.

\(\text { So, }\) \(k_{ eq }=\frac{2 k \times k}{2 k+k}\)

\(=\frac{2 k \times k}{3 k}=\frac{2}{3} k\)

\(T=2 \pi \sqrt{\frac{m}{k_{e q}}}\)

\(\Rightarrow T=2 \pi \sqrt{\frac{3 m}{2 k}}\)