Given this RLC filter circuit:

Producing this transfer function:



Stimulated at 3 different frequencies:

I have this bode plot of frequency and magnitude response:



And for each of the test frequencies, I have a plot of the log-scaled transfer function, input stimulation, output based on convolution of the input stimulation and transfer function (blue) and steady state output of the transfer function (magenta) derived by replacing the ‘s’ in the transfer function by the angular frequency times j (s=jω). Note how after the initial transient response, the convolution output catches up with the steady state output. How quickly it does this depends on the filter.





