Setup: Spring with natural length L_0, spring constant k. Extension/compression: x = deformation from natural length.

Work done by spring from x_1 to x_2: W_spring = (1/2)kx_1^2 - (1/2)kx_2^2

Note: This is (initial PE - final PE), which equals -delta_PE.

Special cases:

1. Stretching from 0 to x: W = -(1/2)kx^2 (spring does negative work)
2. Releasing from x to 0: W = +(1/2)kx^2 (spring does positive work)
3. Stretching from x to 2x: W = -(1/2)k(4x^2-x^2) = -(3/2)kx^2

Common JEE trap: Work to stretch from natural length to x is (1/2)kx^2. But work to stretch from x to 2x is NOT another (1/2)kx^2 — it is (3/2)kx^2 (three times as much!). Spring force increases with extension.

Maximum compression/extension: When all KE is converted to spring PE: (1/2)mv^2 = (1/2)kx_max^2, x_max = v*sqrt(m/k).