Question

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

• A. 1.5 m
• B. 1 m
• C. 0.1 m
• D. 0.5 m

Answer 1

Answer: (B)

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