A flat horizontal board moves up and down under $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........
Medium
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(b)
Maximum acceleration of the system $\left(a_{\max }\right)=-\omega^2 A$
For a block to escape the board the acceleration must be equal to 9 at the top-most point.
$g=\omega^2 A$
$\omega=\sqrt{\frac{g}{A}}$
Time period $=\frac{2 \pi}{\omega}=\sqrt{\frac{A}{g}}$
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