A particle executes simple harmonic motion with amplitude \(A.\) It takes \(4~\text{s}\) to move from the negative extreme position \(-A\) to the position \(x=\dfrac{A}{2},\) moving toward the positive extreme. What is the time period \(T\) of its motion?
1. \(4\) s
2. \(8\) s
3. \(12\) s
4. \(18\) s

The displacement \( x\) of a particle varies with time \(t\) as \(x = A sin\left (\frac{2\pi t}{T} +\frac{\pi}{3} \right)\)$\mathrm{}$. The time taken by the particle to reach from \(x = \frac{A}{2} \) to \(x = -\frac{A}{2} \) will be: