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Question

In figure $(\mathrm{A})$, mass '$2 \mathrm{~m}^{\text {' }}$ is fixed on mass '$\mathrm{m}$ ' which is attached to two springs of spring constant $\mathrm{k}$. In figure (B), mass '$\mathrm{m}$' is attached to two springs of spring constant '$\mathrm{k}$' and '$2 \mathrm{k}^{\prime}$. If mass '$\mathrm{m}$' in (A) and in (B) are displaced by distance '$x^{\prime}$ horizontally and then released, then time period $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ corresponding to $(\mathrm{A})$ and (B) respectively follow the relation.

$$ \frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{3}{\sqrt{2}} $$
$$ \frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{3}{2}} $$
$$ \frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{2}{3}} $$
$$ \frac{T_{1}}{T_{2}}=\frac{\sqrt{2}}{3} $$

Solution

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