Answer
$400$ N/m
Work Step by Step
Let us consider a constant $k$ to express a natural length with limits $0$ to $3$ such that
$\int_0^3 kx dx=1800$
Now, integrate.
$\int_0^3 kx dx=1800 \implies k[ \dfrac{x^2}{2}]_0^3 =1800$
or, $k[ \dfrac{3^2}{2}-0] =1800 \implies k=\dfrac{1800 \times 2}{9}=400$
