Question 83: Oscillations

Question

In figure $$(\mathrm{A})$$, mass '$$2 \mathrm{~m}^{	ext {' }}$$ 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.

Accepted Answer

Both the springs are in parallel combination in both the diagrams so
$${T_1} = 2\pi \sqrt {{{3m} \over {2k}}} $$
and $${T_2} = 2\pi \sqrt {{m \over {3k}}} $$
So, $${{{T_1}} \over {{T_2}}} = {3 \over {\sqrt 2 }}$$

Answer

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

Answer

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

Answer

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

Answer

$$
\frac{T_{1}}{T_{2}}=\frac{\sqrt{2}}{3}
$$

Oscillations

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