1. The problem statement, all variables and given/known data A spring balance consists of a pan that hangs from a spring. A damping force F_d = -bv is applied to the balance so that when an object is placed in the pan it comes to rest in the minimum time without overshoot. Determine the required value of b for an object of mass 2.5 kg that extends the spring by 0.06m. 2. Relevant equations (ω_0)^2 = k/m = ϒ^2/4 b = 2*sqrt(k*m) 3. The attempt at a solution So if we find k, the spring constant, we find b which is what we are looking for. We know the mass is 2.5 kg We know that the change in x is 0.06m. We know that there is critical damping. I need to use the change in x information to find b and/or k. The general solution for crit. damping is x = Ae^(-ϒt/2)+Bte^(-ϒt/2) So the derivative, which is the rate of change is equal to dx/dt = e^(-ϒt/2)(B-ϒBt/2-ϒA/2) max displacement occurs when dx/dt is equal to 0. 0 = e^(-ϒt/2)(B-ϒBt/2-ϒA/2) 0.06 = Ae^(-ϒt/2)+Bte^(-ϒt/2) Am I heading in the right direction here? Is there anything that I am missing in my steps that might lead me in the right direction?