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  4. 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

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Q. 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

AIIMSAIIMS 2007Oscillations

Solution:

Here, $a\, = \,1 \,cm = 0.01\, m$Íž The mass will remain in contact with surface, if
$mg=m\omega^{2}a$ or $\omega=\sqrt{g/a}$
or $2\pi\upsilon=\sqrt{g/a}$ or $\upsilon=\frac{1}{2\pi}\sqrt{\frac{g}{a}}$
$\upsilon=\frac{7}{2\times22}\sqrt{\frac{980}{1}}=4.9\,s^{-1}=5\,Hz$