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We have x = a sin(ωt + π/6). Velocity, v = dx/dt = aω cos(ωt + π/6). Maximum velocity = aω. According to question, aω/2 = aω cos(ωt + π/6).

1. cos(ωt + π/6) = 1/2
2. cos 60° or cos π/3
3. wt + P/3 = P/6
4. wt = P/3 or wt = P/6

Correct answer: cos(ωt + π/6) = 1/2

Solution

The equation aω/2 = aω cos(ωt + π/6) simplifies to cos(ωt + π/6) = 1/2, which directly matches option A.

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