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  4. A piston is performing S.H.M. in the vertical direction with a frequency of 0.5 Hz. A block of 10 kg is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is

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Q. A piston is performing S.H.M. in the vertical direction with a frequency of 0.5 Hz. A block of 10 kg is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is

KCETKCET 2019Oscillations

Solution:

$f=0.5 Hz$
$\omega=2 \pi f=\pi$
for block to remain in contact with the piston at amplitude position weight A the block = Force due to oscillation.
mg = ma
$mg=m\left(\omega^{2}A\right)$
$A=\frac{g}{\omega^{2}}=\frac{10}{\pi^{2}}=1 m$