A particle is executing simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Its time period of vibration will be:
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Question

A particle is executing simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Its time period of vibration will be:

G1 Physics · Accepted Answer

Step 1: Maximum speed vₘₐₓ = ωA = β. Step 2: Maximum acceleration aₘₐₓ = ω²A = α. Step 3: Divide: α/β = ω. Step 4: T = 2π/ω = 2πβ/α. Final answer: (D) 2πβ/α.