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(D) The equation for displacement in simple harmonic motion starting from the mean position is given by $y = A \sin(\omega t)$,where $\omega = \frac{2

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$\frac{1}{3} \ s$

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(D) The equation for displacement in simple harmonic motion starting from the mean position is given by $y = A \sin(\omega t)$,where $\omega = \frac{2\pi}{T}$.Given $T = 4 \ s$,we have $\omega = \frac{2\pi}{4} = \frac{\pi}{2} \ rad/s$.We need to find the time $t$ when the displacement $y = \frac{A}{2}$.Substituting these values into the equation: $\frac{A}{2} = A \sin(\frac{\pi}{2} \cdot t)$.This simplifies to $\sin(\frac{\pi}{2} \cdot t) = \frac{1}{2}$.Since $\sin(\frac{\pi}{6}) = \frac{1}{2}$,we equate the arguments: $\frac{\pi}{2} \cdot t = \frac{\pi}{6}$.Solving for $t$: $t = \frac{1}{3} \ s$.

The periodic time of a particle doing simple harmonic motion is $4 \ s$. The time taken by it to go from its mean position to half the maximum displacement (amplitude) is

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