Question

A horizontal platform is executing simple harmonic motion in the vertical direction with frequency $f$. A block of mass $m$ is placed on the platform. What is the maximum amplitude of oscillation so that the block is not detached from it ?

• A. $\frac{g}{4{\pi }^2{f}^2}$
• B. $\frac{mg}{4{\pi }^2{f}^2}$
• C. $\frac{g}{2{\pi }^2{f}^2}$
• D. $\frac{mg}{2{\pi }^2{f}^2}$

Answer 1

The correct option is A $\frac{g}{4{\pi }^2{f}^2}$

The block will not be detached from the platform, if the amplitude of the platform's SHM is such that the maximum acceleration equals the acceleration due to gravity.
i.e. ${\omega }^2{A}_{\text{max}}=g$
or $A_{\text{max}}=\frac{g}{{\omega }^2}=\frac{g}{4{\pi }^2{f}^2}$
Hence, the correct choice is (a).

Note that $A_{\text{max}}$ is independent of the mass of the block.