A large horizontal surface moves up and down in $S.H.M.$ with an amplitude of $1\, cm$. If a mass of $10\, kg$ (which is placed on the surface is to remain continuously in contact with it, the maximum frequency of $S.H.M.$ will be .... $Hz$
AIIMS 2007, Medium
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Frequency of $SHM,$
$v=\frac{1}{2 \pi} \sqrt{\frac{\text { acceleration }}{\text { displacement }}}=\frac{1}{2 \pi} \sqrt{\frac{a}{x}}$
$\Rightarrow v=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}$
$\Rightarrow \frac{k}{m}=\frac{a}{x} \Rightarrow \frac{k}{a}=\frac{m}{x} \Rightarrow v=\frac{1}{2 \pi} \sqrt{\frac{m}{x}}$
$\Rightarrow \frac{1}{2 \pi} \sqrt{\frac{10}{10^{-2}}}=\sqrt{\frac{10^{3}}{2 \pi}}=\frac{10 \sqrt{10}}{2 \pi}$
$=\frac{10 \times 3.16}{2 \times 3.14}=5 \mathrm{Hz}$
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