A particle undergoing simple harmonic motion has time period T. How much time does it take to travel from its equilibrium (mean) position to a displacement equal to half the amplitude?

T/4
T/8
T/12
T/6

Correct answer: T/12

Solution

In SHM, displacement from mean position: x = A*sin(2*pi*t/T). For x = A/2: sin(2*pi*t/T) = 1/2, so 2*pi*t/T = pi/6, giving t = T/12.

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