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JEE Main 2023 (24 Jan, Shift 2) · Spring Systems

Spring Systems question from JEE Main 2023 (24 Jan, Shift 2)

Q52JEE Main 2023 · 24 JAN · SHIFT 2Medium

Spring Systems

A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases by one second, the value of mass m is ___________ kg.

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

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Answer: 1

$T = 2\pi\sqrt{m/k}$ , so $T \propto \sqrt{m}$ .
$\frac{T_2}{T_1} = \frac{2}{1} = \sqrt{\frac{m+3}{m}} \Rightarrow m + 3 = 4m$
$m = 1$ kg

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