All the springs in fig (a), (b) and (c) are identical, each one… | MHT CET 2026 (18 Apr, Shift 1)

Q18MHT CET 2026 · 18 APR · SHIFT 1Medium

Spring Systems

All the springs in fig (a), (b) and (c) are identical, each one having force constant K. Mass m is attached to each system. If $T_a, T_b$ and $T_c$ are the periodic time of oscillations of the three systems in fig (a), (b) and (c) respectively, then

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Answer: (d)

(a) single spring: $T_a = 2\pi\sqrt{m/K}$ .
(b) series, $K/2$ : $T_b = \sqrt{2}\,T_a$ . (c) parallel, $2K$ : $T_c = T_a/\sqrt{2}$ .
$\frac{T_b}{T_c} = \frac{\sqrt{2}}{1/\sqrt{2}} = 2$ , so $T_b = 2T_c$ .
So the answer is (d).

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