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Question 31191
JEE Physics · Hard

Simple Harmonic Motion: SHM Advanced MCQ

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SHM AdvancedHardQuestion 31191

Question

A particle in SHM has v₁ = 4 cm/s at x = 3 cm and v₂ = 3 cm/s at x = 4 cm. Amplitude A and ω are:
  1. A
    A = 5 cm, ω = 1 rad/s
    Correct
  2. B
    A = 4 cm, ω = 3/4 rad/s
  3. C
    A = 3 cm, ω = 4/3 rad/s
  4. D
    A = 5 cm, ω = 2 rad/s

Correct answer

A = 5 cm, ω = 1 rad/s

Explanation

v² = ω²(A²−x²): 16 = ω²(A²−9) and 9 = ω²(A²−16). Dividing: 16/9 = (A²−9)/(A²−16). 16A²−256 = 9A²−81 → 7A² = 175 → A² = 25 → A = 5 cm. ω² = 16/(25−9) = 1 → ω = 1 rad/s.

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