1. The problem statement, all variables and given/known data
This question came up in a computer science / robotics exam and I still don't know the solution for it. I figured out that it's classical mechanics related, so I thought this might be the best place to ask it.

2. Relevant equations
C = A*x + B*dx/dt

3. The attempt at a solution
I've figured out that the steady state doesn't change, as it happens when dx/dt is 0, thus B is not affecting the solution.

And this is how far I understand it. Can you explain to me, what kind of movement is this, what is the real-life meaning of the steady state and half-life for this movement and that how to calculate the change in the half-life?

Thanks for the help! Actually, I'm not a Physics student, so I don't really know, but I'd guess it's the exponential delay. So if B doubles then the constant becomes half, thus the half-life becomes double. Is this correct?