JEE Main 2014PhysicsOscillationsHardMCQ

JEE Main 2014 — Oscillations Question with Solution

JEE Main 2014 (06 Apr)

Question

A particle moves with simple harmonic motion in a straight line. In first τ s , after starting from rest it travels a distance a, and in next τ s  it travels 2a, in same direction, then :

Choose an option

Show full solutionCorrect option: D
Correct answer
DTime period of oscillations is 6 τ

Step-by-step explanation

           x = - A cos ω t

- A + a = - A cos ω τ                ...(i)

- A + 3 a = - A cos ω 2 τ          ...(ii)

∴    - 1 + a A = - cos ω τ              ...(iii)

and - 1 + 3 a A = - cos 2 ω τ           ...(iv)

Adding (iii) and (iv)

2 = 3  cos ω τ - 2  cos 2 ω τ + 1

∴    2  cos 2 ω τ - 3  cos ω τ + 1 = 0

∴    cos ω τ = 1 2

∴        ω τ = π 3

∴         T = 6 τ

 

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About this question

This is a previous-year question from JEE Main 2014, 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.