Hi everyone,
As you work through the assignment on Circuits, you will come across questions about damping, and you may notice that we never spoke about this in class. Figuring out whether a circuit is over-, under- or critically damped is straightforward, and depends on the discriminant of the characteristic equation — the discriminant is the part under the radical sign when you use the quadratic formula (it controls the number and type of solutions to the quadratic equation):
The Discriminant
- Under-damped: Discriminant < 0 (the characteristic equation has two complex roots)
- Critically Damped: Discriminant = 0 (the characteristic equation has a repeated root)
- Over-damped: Discriminant > 0 (the characteristic equation has two distinct real roots)
But that’s cheating! What does damping actually mean?
Great question! We will not discuss damping in detail in this class, but if you work with electrical circuits this is a concept you will run into often. Take a look here for a basic overview: http://en.wikipedia.org/wiki/Damping
Hope your Spring Break is going well,
Prof. Reitz
