Calculate spring constant - Euler's Method

Can anyone solve this?

A physical system composed of a mass connected by a spring to a fixed point and moving without friction on a horizontal line can be described by the following differential equation:

$\displaystyle m\,\frac{d^2x}{dt^2} + c\, \frac{dx}{dt} + k\, x = 0$

This equation was integrated numerically by Euler's method, using the following values:

t0 m c dx/dt (initial)

0 20 1 1

The results are presented in the graph of position (x) versus time (t), where each point is the result of an iteration.

http://img23.imageshack.us/img23/8320/imgrk.jpg

http://img23.imageshack.us/i/imgrk.jpg/Any help is greatly appreciated. I can tell you that the answer is K = 40, but I don't know how to get there...

My failed attempt at this:

Using maxima:

> 20*'diff('diff(x, t), t) + 'diff(x, t) + K*x;

> ode2(%, x, t);

> ic2(res, t=0, x=1, 'diff(x,t)=1);

> solve(%, K);

But this yields something that doen't make sense...