How to get the absolute value of a function?

So I have to make a plot and phase diagram of the damped oscillation equation:

d^2x/dt^2 + k*sqrt(abs(dx/dt)) + w^2 * x = A * cos(W * t)

So I made two functions fnf and fng, where

fnf = y 

fng = - k * sqrt(abs(dx/dt)) - w^2 * x + A * cos(W * t).

Now the weird part is, when the k value of a normal damped oscillation becomes higher, it damps. However, if I increase the k value of the equation above, the graph goes down. So if k=0, the graph is bounded by y=5 and y=-5 (a cosine), if k>0, then the graph is bounded by y~5 and y<<-5. Am I doing something wrong, or is this actually correct? I used the EXACT same equations as above.

Personally, I think it is the abs(y) that is causing problems.