A block of massm, initally at rest is dropped from a height h onto a spring whose force constant is K. Find the maximum distance x through which the spring will be compressed.

Explanation

When the spring is compressed through distance x, the mass m drops through a distance `(h+x)`
`:.` Potential energy of spring
`=(1)/(2)Kx^(2)=mgh(h+x)`
or `(1)/(2)Kx^(2)-mgx-mgh=0`
or `x^(2)-(2mg)/(K)x-(2mgh)/(K)=0`
`:. x=(2mg)/(K)+-sqrt([((2mg)/(K))^(2)+(8mgh)/(K)])`