Maximum acceleration of the system \(\left(a_{\max }\right)=-\omega^2 A\)

For a block to escape the board the acceleration must be equal to 9 at the top-most point.

\(g=\omega^2 A\)

\(\omega=\sqrt{\frac{g}{A}}\)

Time period \(=\frac{2 \pi}{\omega}=\sqrt{\frac{A}{g}}\)