Question

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

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

Answer 1

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

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.
${\omega }^2{A}_{max}=gOr{A}_{max}=\frac{g}{{\omega }^2}=\frac{g}{4{\pi }^2{v}^2}$
Hence the correct choice is (a). Notice that $A_{max}$ is independent of the mass of the block.