The vertical motion of a huge piston in a machine is approximately SHM with a frequency of 1Hz.A block of mass 20 kg is placed on the piston . What is the maximum amplitude of the piston's SHM for the block and the piston to remain together .
Hint `:` `v= (1)/( 2pi)sqrt((k)/(m))`
Find k
For maximum displacement ` x_(max) =A`
For maximum restoring force , `F= - kA = -mg`
`:. A = (mg)/(k) = (mg) /( momega^(2))= (g)/( omega^(2))`

Explanation

`v= 1 Hz, m= 20 kg , a= ?`
`v= (1)/(2pi) sqrt((k)/(m))`
`:. k = 4 pi^(2) mv^(2)`
For maximum displacement ,` x_(max) = A`
Maximum restoring force ,`F= - kA = -mg`
`:. A= (mg)/(k) = (mg)/(4pi^(2) mv^(2))= (g)/( 4pi^(2) v^(2))`
`= ( 9.8 )/( 4 xx ( 3.14) ^(2) xx (1)^(2)) = 0.2475 m`