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JEE Main 2023 · 25 Jan · Shift 2

JEE Main 2023 Physics question on Oscillations and Waves

A particle executes simple harmonic motion between x=−Ax = -A and x=Ax = A. If time taken by particle to go from x=0x = 0 to A2\frac{A}{2} is 2 s; then time taken by particle in going from x=A2x = \frac{A}{2} to AA is
  1. A.
    3 s
  2. B.
    1.5 s
  3. C.
    2 s
  4. D.
    4 s
Show answer and solution

Correct option: D

Solution

In SHM, x = A sin(ωt). Time to go from x = 0 to x = A/2: A/2 = A sin(ωt₁), so sin(ωt₁) = 1/2, giving ωt₁ = π/6, so t₁ = 2 s means ω = π/12 rad/s.

Time to go from x = 0 to x = A: ωt₂ = π/2, so t₂ = (π/2)/ω = (π/2)/(π/12) = 6 s.

Time from x = A/2 to x = A = t₂ − t₁ = 6 − 2 = 4 s.

[JEE Main 2023 · 25 Jan · Shift 2]

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