Answer
$a = 7.9~m/s^2$
Work Step by Step
We can find $\omega$:
$T = \frac{2\pi}{\omega}$
$\omega = \frac{2\pi}{T}$
$\omega = \frac{2\pi}{0.50~s}$
$\omega = 4\pi~rad/s$
At the point of maximum extension of the spring, the magnitude of acceleration is at its maximum. We can find the magnitude of the acceleration:
$a = A~\omega^2$
$a = (0.050~m)~(4\pi~rad/s)^2$
$a = 7.9~m/s^2$
