Write an equation for the work necessary to stretch the spring from the relaxed state to distance x1

The equation stems from the principle concept of Hooke's Law. After derivation, the general equation for finding the work of a stretch spring is written below:

W = k[ (x₂ - x₁) + (x₁ - xn) ]

where

k is the spring constant

xn is the natural length of the spring

x₁ is the length after stretching

x₂ is the length after stretching even further

Suppose the spring was only stretched once, then x₁ = x₂. The equation is simplified to:

W = k (x₁ - xn)