The vertical motion of a huge piston in a machine is approximately simple harmonic with a frequency of `0.50 s^(-1)`. A block of 10 kg is placed on the pistion. What is the maximum amplitude of the pistion's SHM for the block and the piston to remain together ?

Explanation

Given, `v=0.5s^(-1), g=9.8ms^(-1)
alpha=omega^(2)y=(2piv)^(2)y = 4pi^(2)v^(2)`y
`a^(max)` at the extreme position i.e, `r=y`
`a^(max) = 4pi^(2)v^(2)r and a^(max)= g` to remain in contact. Or `r = g/(4pi^(2)v^(2))=9.8/(4pi^(2) ** (0.5)^(2))=0.993m`.