Question

A horizontal platform is executing simple harmonic motion in the vertical direction of frequency $\nu$. 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 form it?

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

Answer 1

Answer: (A)

$\frac{g}{4{\pi }^2{\nu }^2}$

The maximum acceleration of mass $m$ is $-{\omega }^2\times a$

where $a$ is the amplitude of SHM and $\omega =2\pi \nu$ is the angular frequency.

So, the maximum amplitude of the platform so that the block is not detached is given as $-{\omega }^2\times a=-g\Rightarrow a=g/4{\pi }^2{\nu }^2$