Physics - SHM Question with Solution | TestHub

For the object not to detach from the platform, the maximum downward acceleration of the platform must be less than or equal to the acceleration due to gravity $g$.

$a_{\text{max}}\le g$

For the least period, the angular frequency $\omega$ is maximum, which corresponds to the limiting case $a_{\text{max}}=g$.

${\omega }^{2}A=g$

${\left(\frac{2\pi }{T}\right)}^{2}A=g$

$T=2\pi \sqrt{\frac{A}{g}}$

Given $A=40\text{ cm}=0.4\text{ m}$ and $g=10{\text{ m/s}}^2$.

$T=2\pi \sqrt{\frac{0.4}{10}}$

$T=2\pi \sqrt{0.04}$

$T=2\pi \times 0.2=0.4\pi \text{ s}$

Answer: $0.4\pi \mathrm{s}$