- #1
RJLiberator
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Homework Statement
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.
Homework Equations
(ω_0)^2 = k/m = ϒ^2/4
b = 2*sqrt(k*m)
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?