A spring of force constant `k` is stretched by a small length `x`. Find the work done in stretching it further by a small length `y`.

Explanation

Let `W_(1)` is the work done in stretching a spring of force constant .K. through a length ..x... Then `W_(1)=(1)/(2)Kx^(2)`
Let `..W_(2)..` is the workdone in stretching the spring through a length `(x+y)`. Then `W_(2)=(1)/(2)K(x+y)^(2)`
`therefore` Additional work done, to increase the elongation by ..y.. is `W=W_(2)-W_(1)`
`W=(1)/(2)K(x+y)^(2)-(1)/(2)Kx^(2)`
`therefore W=(1)/(2)Ky (y+2x)`