JEE Main 2023PhysicsOscillationsEasyNumerical

JEE Main 2023 — Oscillations Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

A block of mass 2 kg is attached with two identical springs of spring constant 20 N m-1 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 πX in SI unit. The value of X is______.

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

When the block is displaced by a distance x, force acting on block due to both springs will be in the same direction. Therefore,

F=-2kx⇒a=-2kmx,

Comparing it witha=-ω2x , we get

ω=2km=2×202

=20 rad s-1

Now, T=2πω=2π20=π5

Hence, required value of X=5.

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About this question

This is a previous-year question from JEE Main 2023, covering the Oscillations chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.