A piston is performing S.H.M. in the vertical | vedclass

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(B) Given frequency $f = 0.5 \,Hz$.Angular frequency $\omega = 2 \pi f = 2 \pi (0.5) = \pi \,rad/s$.For the block to remain in contact with the piston

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(B) Given frequency $f = 0.5 \,Hz$.Angular frequency $\omega = 2 \pi f = 2 \pi (0.5) = \pi \,rad/s$.For the block to remain in contact with the piston, the downward acceleration of the piston at the extreme position must not exceed the acceleration due to gravity $g$.The condition for the block to just lose contact is $a_{max} = g$.Since $a_{max} = \omega^2 A$, we have $\omega^2 A = g$.Substituting the values, $\pi^2 A = 10$.Taking $\pi^2 \approx 10$, we get $10 A = 10$.Therefore, $A = 1 \,m$.

$A$ 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: (in $\,m$)

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