Let's say you have a second-order low-pass or high-pass filter with a reasonable Q factor. I am curious as to why the relaxation oscillation frequency 'w0' does not provide the peak value in magnitude, but rather that frequency is equal to: (low-pass)

\(w_{max} = w_{0}\sqrt{1 - \frac{1}{2Q^{2}}}\) Slightly less than w0 for Q > 0.5.

I know that this is what the math works about to be for these filters, but in terms of physically what is going on, wouldn't it make more sense that the relaxation oscillation frequency would have the highest peak?

If you injected a signal at the same frequency as w0 (in phase), wouldn't it resonate much more effectively than if the injected frequency was at this so called 'wmax'?

Thanks!