A block is resting on a piston which is moving vertically with simple harmonic motion of period 1.0 second. At what amplitude of motion will the block and piston separate? What is the maximum velocity of the piston at this amplitude?

Explanation

Restoring force `=momega^(2)a,`
weight of block `=mg`
For just separation of block and piston,
`momega^(2)a=mg`
or `a=(g)/(omega^(2))=(gT^(2))/(4pi^(2))=(9.8xx(1.0)^(2))/(4xx(3.14)^(2))=0.25m`
Max. velocity of block,
`V_(max.)=aomega=0.25xx2pi//T`
`=0.25xx2xx3.14//1=1.57ms^(-1)`