JEE Main 2015PhysicsOscillationsHardMCQ

JEE Main 2015 — Oscillations Question with Solution

JEE Main 2015 (10 Apr Online)

Question

A simple harmonic oscillator of angular frequency 2 rad s-1 is acted upon by an external force F=sin⁡t N. If the oscillator is at rest in its equilibrium position at t=0, its position at later times is proportional to:

Choose an option

Show full solutionCorrect option: C
Correct answer
Csin⁡t-12sin⁡2t

Step-by-step explanation

It is given that oscillator at rest at t=0 i.e. at t=0, v=0. So, in option, we can check by putting v=dxdt=0.

(1) If x∝sin⁡t+12cos⁡2t

⟹v∝cos⁡t+12×2 (-sin⁡2t)

⟹  at t=0, v∝1-0≠0

(2) If x ∝cos⁡t-12sin⁡t

⟹  v∝-sin⁡t-12cos⁡t

⟹at t=0, v∝-12≠0

(3) If x∝sin⁡t-12 sin 2t

then υ∝cos⁡t-12×2cos⁡2t

⟹at t=0, v∝1-1=0

(4) If x∝sin⁡t+12sin⁡2t

⟹v∝cos⁡t+12×2cos⁡2t

⟹at t=0, v∝1+1

⟹  v∝2≠0

∴   in option 3  v=0   at   t=0

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About this question

This is a previous-year question from JEE Main 2015, 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.