A particle executes simple harmonic motion of time period T . At t = 0 , it is at rest and moves towards positive amplitude then :-

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The velocity will be again zero after phase $π$ so taken time will be $T /2$ For $v = \frac{v _{max}}{2}$ $\Rightarrow ω A^{2} - x^{2} = \frac{A ω}{2} \Rightarrow x = \pm \frac{3 A}{2}$ So particle phase would be changed $\frac{π}{6}$ i.e. it will take time $= \frac{T}{12}$

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