Thanks for the great lecture with many physical insights related to second order systems. The distinction of omega_n, omega_r and omega_d is often not mentioned so it was refreshing to see it highlighted. I noticed that at around 25:05, the sqrt(2) that is marked on the vertical axis should be sqrt(2)/2 or 1/sqrt(2).
Very nice rundown of second order filter characteristics! It's definitely musically useful that the bandwidth of the resonance peak widens in proportion to the natural frequency, but I think it's also very natural: The Q parameter controls the shape of the frequency response, while the natural frequency just changes the frequency scale, or equivalently, the time scale, making the whole filter faster or slower. So I guess that it is this process of time scale change that corresponds very naturally to our logarithmic perception of frequency.
Brilliantly done! Thank you! I also had assumed that the ripples on the oscilloscope correspond to the peak in the transfer function. Very interesting to learn that that's not actually correct!
