JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Elasticity & SHM

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In figure (A), mass '2m' is fixed on mass 'm' which is attached to two springs of spring constant k. In figure (B), mass 'm' is attached to two spring of spring constant 'k' and '2k'. If mass 'm' in (A) and (B) are displaced by distance 'x' horizontally and then released, then time period

T_{1}

and

T_{2}

corresponding to (A) and (B) respectively follow the relation.

(A) $\frac{T _{1}}{T _{2}} = \frac{3}{2}$ ✓ Correct
(B) $\frac{T _{1}}{T _{2}} = \frac{3}{2}$
(C) $\frac{T _{1}}{T _{2}} = \frac{2}{3}$
(D) $\frac{T _{1}}{T _{2}} = \frac{2}{3}$

Answer: (A)

Solution

Figure (A): Total mass =

3 m

, effective spring constant =

2 k

(two springs in parallel).

T_{1} = 2 π \frac{3 m}{2 k}

Figure (B): Mass =

m

, effective spring constant =

k + 2 k = 3 k

(two springs in parallel).

T_{2} = 2 π \frac{m}{3 k}

Ratio:

\frac{T _{1}}{T _{2}} = \frac{2 π \frac{3 m}{2 k}}{2 π \frac{m}{3 k}} = \frac{3 m}{2 k} \times \frac{3 k}{m} = \frac{9}{2} = \frac{3}{2}

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JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Elasticity & SHM

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