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(D) The equation of motion for a particle in simple harmonic motion starting from the mean position $(x = 0)$ is given by $x = A \sin(\omega t)$.For $

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$4$

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(D) The equation of motion for a particle in simple harmonic motion starting from the mean position $(x = 0)$ is given by $x = A \sin(\omega t)$.For $x = \frac{A}{2}$, we have $\frac{A}{2} = A \sin(\omega t_1)$, which implies $\sin(\omega t_1) = \frac{1}{2}$.Thus, $\omega t_1 = \frac{\pi}{6}$. Given $t_1 = 2 	ext{ s}$, we get $\omega(2) = \frac{\pi}{6}$, so $\omega = \frac{\pi}{12} 	ext{ rad/s}$.Now, for $x = A$, we have $A = A \sin(\omega t_2)$, which implies $\sin(\omega t_2) = 1$.Thus, $\omega t_2 = \frac{\pi}{2}$. Substituting $\omega = \frac{\pi}{12}$, we get $t_2 = \frac{\pi/2}{\pi/12} = 6 	ext{ s}$.The time taken to go from $x = \frac{A}{2}$ to $x = A$ is $\Delta t = t_2 - t_1 = 6 	ext{ s} - 2 	ext{ s} = 4 	ext{ s}$.

$A$ particle executes simple harmonic motion between $x = -A$ and $x = +A$. If time taken by particle to go from $x = 0$ to $x = \frac{A}{2}$ is $2 \text{ s}$, then time taken by particle in going from $x = \frac{A}{2}$ to $x = A$ is (in $\text{ s}$)

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