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 streching a spring of force constant .K. through a length ..x... Then `W_(1) = (1)/(2) Kx^(2)` Let ..`W_(2)..` is the workdone in streching 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)`
`thereforeW=(1)/(2)Ky(y+2x)`