Q: A spring of force constant ‘k’ is stretched by a small length ‘x’. Find work done in stretching it further by a small length ‘y’?

Sol: Initial potential energy $\large U_i = \frac{1}{2} k x^2 $

Final potential energy $\large U_f = \frac{1}{2} k (x + y)^2 $

Work done $\large W = U_f – U_i = \frac{1}{2} k (x + y)^2 – \frac{1}{2} k x^2 $

$\large W = \frac{1}{2}k (y^2 + 2 x y) $