An elastic spring of unstretched length L and force constant k is stretched by a small length x. It is further stretched by another small length y. Work done during the second stretching is

Explanation

Initial potential energy `U_(i) = 1/2 kx^(2)`
Final potential energy `U_(f) = 1/2 k(x + y )^(2)`
Work done
`W = U_(f) - U_(i) = 1/2 k(x+ y )^(2) - 1/2 kx^(2)`
`W = 1/2 ky (2x + y)`