Yeah you missed one case didnt you? The oscillator. THAT is the system. The signal (cosine) and the system (oscillator) have the same equation. There's no way around this because they produce the same math function!

Again, you're confusing system with signal. In the case of the oscillator, the system -- as a differential equation -- will have a solution that is a cosine. But the system itself is definitely not a cosine.

So now you say that 1-e^(-A*t) is linear? Make up your mind what you want to call linear.

Sigh. I'm guessing that's the expression for the voltage response -- a signal -- across the resistor in an RL circuit fed with a step input. The inductor is not a signal, it is a system: we can characterize it with a differential equation. Do you understand the distinction between a differential equation and its solutions? This is effectively the same difference between a system and signal. Just as linear DEs can have solutions that are nonlinear functions, so can linear systems produce nonlinear responses. If that doesn't help see the difference, try this: if the thing in question has an input and an output, it is a system; otherwise, it's probably a signal.

 

But another one is from circuit analysis, where we have say an inductor which has response in the time domain that is not considered linear but in the frequency domain it is. For example an inductor in series with a resistor. The response is non linear in time but linear in frequency.

The response of an inductor or resistor-inductor circuit in the time domain most certainly is linear. If you measure the response of the circuit to two inputs and then combine those inputs in linear combination, the response will be the same linear combination of the response to the individual inputs. An inductor is a system and that system is linear.

 

The response of an inductor or resistor-inductor circuit in the time domain most certainly is linear. If you measure the response of the circuit to two inputs and then combine those inputs in linear combination, the response will be the same linear combination of the response to the individual inputs. An inductor is a system and that system is linear.

Hi,

Well he wanted to stick to the "straight line through the origin" definition so that's why i brought this up because an exponential like 1-e^-at is not a straight line through the origin.

 

Hi,

Well he wanted to stick to the "straight line through the origin" definition so that's why i brought this up because an exponential like 1-e^-at is not a straight line through the origin.

That has NOTHING to do with whether an inductor is linear.

Your exponential signal is the RESPONSE of and RL circuit to a PARTICULAR input signal.

By your reasoning, you must also maintain that a resistor is not a linear device since its response to that SAME signal is also not a straight line through the original.

 

That has NOTHING to do with whether an inductor is linear.

Your exponential signal is the RESPONSE of and RL circuit to a PARTICULAR input signal.

By your reasoning, you must also maintain that a resistor is not a linear device since its response to that SAME signal is also not a straight line through the original.

Hi again,

Ok thanks, but then i would be interested to hear how you determine that an LR circuit is linear in time.
I know it is linear in frequency so dont bother going there

And i really am interested to hear your take on this.

I think i see what you are tying to say here. So in that light all we can say about that previous declaration is that the RL circuit response is non linear not the RL itself. I guess i got too used to seeing the networks being tested with step responses and sines and the like.

 

Hi again,

Ok thanks, but then i would be interested to hear how you determine that an LR circuit is linear in time.

Simple. A system is linear if and only if it obeys superposition.