A block of mass 2 kg is attached with two identical springs of spring… | JEE Main 2023 (24 Jan, Shift 1)

Q49JEE Main 2023 · 24 JAN · SHIFT 1Easy

Spring Systems

A block of mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $\frac{\pi}{\sqrt{x}}$ in SI unit. The value of $x$ is ____________.

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Answer: 5

Springs on both sides act in parallel: $k_{eff} = 20 + 20 = 40\text{ N/m}$ .
$T = 2\pi\sqrt{\frac{2}{40}} = \frac{2\pi}{\sqrt{20}} = \frac{2\pi}{2\sqrt{5}} = \frac{\pi}{\sqrt{5}}$
Comparing with $\frac{\pi}{\sqrt{x}}$ : $x = 5$ .

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