What is the maximum frequency for which the penny just barely remains in place for the full cycle in Hz?

Question

A penny rides on top of a piston as it undergoes vertical simple harmonic motion with an amplitude of 4.0 cm. If the frequency is low, the penny rides up and down without difficulty. If the frequency is steadily increased, there comes a point at which the penny leaves the surface. What is the maximum frequency for which the penny just barely remains in place for the full cycle in Hz?

Answer 1

If the acceleration of the piston a exceeds g the penny will leave the surface.
a = omega^2*amplitude
omega = sqrt(g/0.04)
f = omega/(2*pi)