$\frac{ dx }{ dt }= v = A \omega \cos (\omega t )$

$\frac{ dv }{ dt }= a =-\omega^2 A \sin (\omega t )$

$a =-\left(\frac{2 \pi}{8}\right)^2 \times 1 \sin \left(\frac{2 \pi}{8} \times 2\right)$

$\Rightarrow a =-\frac{\pi^2}{16} \times \sin \left(\frac{\pi}{2}\right)$

$\therefore a =\frac{-\pi^2}{16}\,m / s ^2$