In the situation as shown in figure time period of vertical oscillation of block for small displacements will be
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Let block be displaced through $x$ in downward
direction and elongation in spring $=\mathrm{x}_{1}$ then
$x \cos \theta=x_{1}$ $...(1)$
Restoring force $\mathrm{F}=2 \mathrm{kx}_{1} \cos \theta$
$\mathrm{F}=2 \mathrm{k} \cos ^{2} \theta \times$
Hence $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \cos ^{2} \theta}}=2 \pi \sec \theta \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}$
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