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Question 31136
JEE Physics · Hard

Simple Harmonic Motion: Energy Conservation MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Energy ConservationHardQuestion 31136

Question

In SHM, particle has speed v₁ at x₁ and v₂ at x₂. Amplitude is:
  1. A
    √(v₁²−v₂²)/(ω)
  2. B
    √(v₁²x₂²−v₂²x₁²)/(v₁²−v₂²)
  3. C
    √((v₁²x₂²−v₂²x₁²)/(v₁²−v₂²))
    Correct
  4. D
    √(v₁x₁−v₂x₂)

Correct answer

√((v₁²x₂²−v₂²x₁²)/(v₁²−v₂²))

Explanation

v² = ω²(A²−x²). v₁² = ω²(A²−x₁²) and v₂² = ω²(A²−x₂²). Eliminate ω²: A² = (v₁²x₂²−v₂²x₁²)/(v₁²−v₂²).

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