1. The problem statement, all variables and given/known data If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring? 2. Relevant equations Spring constant - f(x) = kx [tex]\int[/tex]ab f(x)dx where a,b are initial and ending positions of the particle and f(x) is the work done in moving from a to b. 3. The attempt at a solution I first tried a non-calculus solution by turning both statements into algebra problems... 6 = (10-x) + (12-x) 6 = 22 - 2x -2x = 16 x = -8 10 = (10-x) + (14-x) 10 = 26-2x -2x = 16 x = -8 Obviously this didn't get me anywhere..