Phase at mean position $=0$

Phase at mid point

$\frac{A}{2}=A \sin \phi$

$\phi=\frac{\pi}{6}$

Time it takes to travel a phase difference of $\phi$

$t=\frac{2 \pi}{\omega} \times \frac{\phi}{2 \pi}$

or $t=\frac{\phi}{\omega}$

or $t=\frac{\pi}{6 \omega}$

Average speed $=\frac{\text { Total distance }}{\text { Time taken }}$

$=\frac{A / 2}{\pi / 6 \omega}$

$=\frac{3 A \omega}{\pi}$