The vertical motion of a huge piston in a machine is approximately SHM. A block of 5 kg is placed on the piston. The maximum amplitude of the piston's SHM for the block and the piston to remains together is 0.99m. Find the frequency .
Hint `:` `v= (1)/( 2pi)sqrt((k)/(m))`
Find k
For maximum displacement ` x_(max) =A`
For maximum restoring force , `F= - kA = -mg`
`:. k= (mg)/( A)`. Put the valeu of K in `v =(1)/( 2pi ) sqrt((k)/(m))` to find v .

Explanation

`v= (1)/( 2pi)sqrt((k)/(m))`
Find k
For maximum displacement ` x_(max) =A`
For maximum restoring force , `F= - kA = -mg`
`:. k= (mg)/( A)`. Put the value of K in `v =(1)/( 2pi ) sqrt((k)/(m))` to find v .