Answer
The maximum amplitude such that the pebble does not lose contact with the board is 3.2 cm
Work Step by Step
We can find $\omega$:
$\omega = 2\pi~f$
$\omega = (2\pi)~(2.8~cycles/s)$
$\omega = 17.6~rad/s$
The magnitude of the maximum acceleration is $\omega^2A$. As long as the acceleration does not surpass $g$, the pebble will stay on the board. We can find the maximum amplitude.
$\omega^2A = g$
$A = \frac{g}{\omega^2}$
$A = \frac{9.80~m/s^2}{(17.6~rad/s)^2}$
$A = 0.032~m = 3.2~cm$
The maximum amplitude such that the pebble does not lose contact with the board is 3.2 cm.
