Question

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

• A. at the highest position of the platform
• B. at the mean position of the platform
• C. for an amplitude of $\frac{g}{{\omega }^2}$
• D. None of these

Answer 1

The correct option is C for an amplitude of $\frac{g}{{\omega }^2}$

The acceleration of the coin in simple harmonic motion is given by:
$a=-{\omega }^{2}X$
The coin will definitely leave contact with platform at maximum x that is when $X=A$
$a=-{\omega }^{2}A$
Now, this acceleration will be be equal to acceleration due to gravity when coin will leave contact
$a=-g-{\omega }^{2}A=-gA=\frac{g}{{\omega }^2}$