Piston Oscillates Vertically

A piston oscillates vertically at 3.7 Hz. Find the maximum oscillation amplitude so a coin resting atop the piston doesn't come off at any point in the cycle.

The max acceleration of piston will be equal to 'g' (9.8m/s^2) because when it has that acceleration, the coin will just be freely falling at the same rate due to gravity, so the coin and piston are just about to lose contact.

Angular velocity, w (omega) = 2.pi.f = 23.2 rad/s
a = -w^2x (ignore sign, not required)
9.8 = 23.2^2x
x = 0.018m (1.8cm)

You place a coin atop the piston. The piston is executing SHM so it is continuously moving up and down with some acceleration. The coin rests on the piston and two forces are acting on it F = mg and the normal in the upward direction. If the acceleration of the SHM of piston exceeds g then apart from F=mg an additional force will act on the coin in the upward direction and the coin will fly away. Hence the maximum acceleration of the SHM should be g.

Frequency = 3.7 Hz.
Angular frequency [ω] = 2 π X frequency
Substituting you get
ω = 23.25 rad/sec
Acceleration = ω^2 X Amplitude
Substituting Amplitude (Maximum) = 9.8/ [23.25]^2 = .0181 m