Question

If 3 J of work are needed to stretch a spring from 11 cm to 13 cm and 5 J are needed to stretch it from 13 cm to 15 cm, what is the natural length of the spring?

Answer 1

what 3 J & 5 J mean?

Answer 2

J=joule
for more information, read
https://en.wikipedia.org/wiki/Joule

Here the two unknowns are
1. spring constant, k (stiffness of spring)
2. natural length, L

The standard relation between stretching and work done (in joules) is
W(x1,x2)=(k/2)(L+x2)^2-k(L+x1)^2
where the string is stretched from L+x1 to L+x2.
L=natural of spring (m)
W=work done (J)
k=spring constant (J/m)

Two equations can be formed, one for each case/observation:
3=(k/2)((L+0.13)^2-(L+0.11)^2)
5=(k/2)((L+0.15)^2-(L+0.13)^2)
Solve the system of equations and find k and L.