A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency `omega`. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

Options

A. at the highest position of the platform
B. at the mean position of the platform
C. for an amplitude of `(g)/(omega^2)`
D. for and amplitude of `sqrt((g)/(omega))`

Answer

A, C

Explanation

Let O be the mean position and a be the acceleration at a displacement x from O
At position I, `N-mg=ma`
`Nne0`
At position II, `mg-N=ma`
For `N=0` (lost of contant), `g=a=omega^2x`.
Loss of contact will occur for amplitude `x_(max)=(g)/(omega^2)` at the highest point of the motion.