Answer
$t=\frac{T}{6}$
Work Step by Step
According to the displacement equation
$x=Acos(\frac{2\pi t}{T})$
but $x=\frac{A}{2}$
$\implies \frac{A}{2}=Acos(\frac{2\pi t}{T})$
$\implies cos(\frac{2\pi t}{T})=\frac{1}{2}$
$\implies \frac{2\pi t}{T}=cos^{-1}(\frac{1}{2})$
$\implies t=\frac{T}{2\pi}cos^{-1}(\frac{1}{2})$
We know that $cos^{-1}(\frac{1}{2})=\frac{\pi}{3}$
$\implies t=\frac{T}{2\pi}(\frac{\pi}{3})$
$t=\frac{T}{6}$
