A coin is placed on a horizontal platform, which undergoes 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

Let O be the mean position and a be the acceleration at a displacement x from O.At position I, N - mg = ma∴ N≠0At position II, mg−N=maFor N = 0 (loss of contact), g=a=ω2xLoss of contact will occur for amplitude xmax=g/ω2 at the highest point of the motion. The coin will leave contact at any point when the acceleration of platform is more than 'g' and in the same direction of 'g'. At the highest point, both of the conditions are satisfied.