A particle executes simple harmonic oscillation with amplitude a and period T. The minimum time to travel half the amplitude from the equilibrium position is:
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Question

A particle executes simple harmonic oscillation with amplitude a and period T. The minimum time to travel half the amplitude from the equilibrium position is:

G1 Physics · Accepted Answer

Step 1: Choose x = a sin(ωt) with the particle crossing equilibrium at t = 0. Step 2: At x = a/2, sin(ωt) = 1/2. The earliest positive phase is ωt = π/6. Step 3: As ω = 2π/T, t = (π/6)/(2π/T) = T/12. Final answer: (B) T/12.