A flat horizontal board moves up and down in $SHM$ of amplitude $\alpha$. Then the shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is
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$\mathrm{m} \alpha \omega^{2}=\mathrm{mg}$
$\omega=\sqrt{\frac{g}{\alpha}}$
$\frac{2 \pi}{\mathrm{T}}=\sqrt{\frac{\mathrm{g}}{\alpha}} \quad \text { or } \quad \mathrm{T}=2 \pi \sqrt{\frac{\alpha}{\mathrm{g}}}$
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