A simple harmonic oscillator has an amplitude a and time period T. The time required for it to travel from x = a to x = a/2 is:
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Question

A simple harmonic oscillator has an amplitude a and time period T. The time required for it to travel from x = a to x = a/2 is:

G1 Physics · Accepted Answer

Step 1: Let x = a cos(ωt), so the oscillator begins at x = a when t = 0. Step 2: At x = a/2, cos(ωt) = 1/2, giving ωt = π/3 for the first passage. Step 3: Time t = (π/3)/(2π/T) = T/6. Final answer: (A) T/6.