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.
Suppose a control system is described by the equation
C = A*x + B*dx/dt
where B is proportional to the mass of the robot. The behaviour of the system can be characterised by the steady state (e.g. the asymptotic velocity of the robot) and the half-life time of the decrease of the distance to the steady state. Explain how the steady state and the half-life change if the mass of the robot is doubled.
I've figured out that the steady state doesn't change, as when dx/dt is 0 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?