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JEE Main 2021 (17 Mar, Shift 1) · Spring Systems

Spring Systems question from JEE Main 2021 (17 Mar, Shift 1)

Q66JEE Main 2021 · 17 MAR · SHIFT 1Easy

Spring Systems

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is Tb/Ta = $\sqrt{x}$ , where value of x is ___________. (Round off to the Nearest Integer)

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Fig. 1: $T_a = 2\pi\sqrt{\frac{M}{k}}$ .
Fig. 2 (series): $k_{eff} = \frac{k}{2}$ , $T_b = 2\pi\sqrt{\frac{2M}{k}}$ .
$\frac{T_b}{T_a} = \sqrt{2}$ , so $x = 2$ .

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