- TL;DR Summary
- Confused by the Pi rads phase lag
Now ... 1) when W is much smaller than Wo the delta phase lag is zero (the driven moves in synch with the driver
2) when W = Wo we have a resonance condition and the phase lag is pi/2
3) when W is much larger than Wo there is a phase lag of pi radians
This can be observed nicely with Barton's pendulae.
The shape of the graph of delta phase lag against w that you find looks like ...
But if you plot a graph of a made up function such as ...
It seems that if you move the negative portion up you get the correct kind of shape but my issue is that inverse tan only goes from -pi/2 to +pi/2 so the inverse tan of anything, whatever it is never approaches pi.
How can this approach be justified? because it almost seems to me that from the maths that if W is very much bigger than Wo then the arctan is negative so rather that a phase lag, if you are changing sign doesn't this suggest a phase lead? Clearly this is not what happens though when you watch the system oscillating and also it can't be anyway, doesn't make sense.
I would love your input on this ...