A block is released from height `h`, find the maximum compression of spring of spring constant `k`.

Explanation

`K_1+U_(g1)+U_(s1)=K_2+U_(g2)+U_(s2)`
`0+mg(h+x)+0=0+0+(1)/(2)kx^2`
`kx^2-2mgx-2mgh=0`
`x=(-(-2)+-sqrt((-2mg)^2-4k(-2mgh)))/(2k)`
`=(mg)/(k)[1+sqrt(1+(2kh)/(mg))]`
Maximum compression `x=x_0=(mg)/(k)[1+sqrt(1+(2kh)/(mg))]`