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 is 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)`