A coin is placed on a horizontal platform which under goes vertical simple harmonic motion of angular frequency ω). The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time:

The coin will be just leaving the contact at the lowest position when ${mω}^{2} A \geq mg \Rightarrow A \geq \frac{g}{ω^{2}}$

A coin is placed on a horizontal platform which under goes vertical simple harmonic motion of angular frequency $ω$ ). The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time: