A particle executes simple harmonic oscillation with an amplitude A. If the time period of oscillation is T, then minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
A
T4
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B
T8
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C
T12
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D
T2
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Solution
The correct option is CT12 Let displacement equation of particle executing SHM is y=A sin ωt As particle travels half of the amplitude from the equilibrium position, so y=A2 Therefore , A2=A sin ωt or sin ωt=12=sin π6 or ωt=π6 or t=π6ω or t=π6(2πT)[asω=2πT] or t=T12 Hence, the particle travels half of the amplitude from the equilibrium in T12s.