im not sure if i did this problem right, something tells me i didnt do it right...could you check my work? thanks in advance.
IMG.pdf
the key here is to treat the natural length of the spring (no stretch) as $\displaystyle x = 0$
stretching the spring 5 cm beyond its natural length ...
$\displaystyle k = \frac{F}{x} = \frac{30 \, N}{.05 \, m} = 600 \, \frac{N}{m}$
work done to stretch the spring 10 cm beyond its natural length ...
$\displaystyle W = \int_0^{0.1} 600x \, dx$
work done to stretch the spring from 20 cm to 30 cm (from 10 cm to 20 cm beyond its natural length) ...
$\displaystyle W = \int_{0.1}^{0.2} 600x \, dx$