Do the rising waveforms for overdamped circuits of different \$\zeta >= 1\$ actually have a different "curviness"? Or does it just look that way because they're all shown on the same time scale?
You know, how you can get any square wave to look like any one of these by adjusting the horizontal scale on the scope. I'm wondering if they actually have more rounded shapes as the damping factor increases or whether they're all exponentials with a different time constant or something and you could overlay one on top of the other if you had a "fine" mode on your scope horizontal controls.
The reason I'm asking is I had the preconception that a waveform for a damping factor of 1.0 was going to be better (like straighter until you got to the top) than one for say 2.0, even if they both exhibited the same rise time. So I was thinking I would have to get my pole placement just right to get about 75° phase shift at exactly the crossover frequency, even if I could have say 85° at crossover without careful tuning.