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The periodic time of a body executing simple harmonic motion is 3 sec. After how much interval from time t = 0, its displacement will be half of its amplitude

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$\frac{1}{3} \sec$

$\frac{1}{8} \sec$

$\frac{1}{6} \sec$

$\frac{1}{4} \sec$

answer is C.

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Detailed Solution

$y = asin \frac{2 π}{T} t$ $\Rightarrow \frac{a}{2} = asin \frac{2 πt}{3}$ $\Rightarrow \frac{1}{2} = \sin \frac{2 πt}{3}$

$\Rightarrow \sin \frac{2 πt}{3} = \sin \frac{π}{6}$ $\Rightarrow \frac{2 πt}{3} = \frac{π}{6}$ $\Rightarrow t = \frac{1}{4} \sec$

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