# Have 'natural response' defined clearly?

some textbook says it is zero input response(response with only initial energy stored). But in other contexts,like response of an RC circuit with only step input (no initial energy) ,the transient part of the solution is called natural response.(I assume voltage across capacitor as response).Please clear my confusion.

This section is from Engineering circuit analysis by Hayt

Now this is from an MIT Lecture

Link of this Lecture Natural Response

• initial conditions must always be known for any response Nov 29, 2017 at 3:22
• Initial energy is zero. Nov 29, 2017 at 3:35
• Natural Response is defined by any disturbance, step, impulse etc. So it is not always zero input but could be, to simplify the explanation. Nov 29, 2017 at 3:40
• I have added some references. Nov 29, 2017 at 4:05
• The natural response is the zero input response, ie the response to initial conditions in the absence of any forcing functions.
– Chu
Nov 29, 2017 at 18:00

There are two possible ways of splitting the system response for analysis:

a) Transient vs Permanent response

b) Natural (zero input) vs Forced (zero state) response

Part of the transient comes from the natural response but there's another part that it's forced from the source. On the other side, the permanent response it's always forced. A good example I did once, and you can do if you still haven't got a grip, is this circuit:

The switch opens in t=0, before it was closed since minus infinity. If you solve it with Laplace you have to be cautelous about the initial conditions while transforming. If you are tidy you will notice that once you have simplified and anti-transformed, the transient has terms that comes from the 'circuit itself' and terms that comes from the transform of the sinusoidal source. Hope you've understood.

P.S. I think that until now you've seen circuits where 100% of the transient comes from the natural response, and the texts you've read used the two concepts (natural and transient) indistinctively. That's the cause of your misinterpretation.

• I think this answer is pretty good quality in general, but you could improve it a little by using the built-in CircuitLab schematic drawing tool instead of a hand drawing. They're editable too! You can find it in the toolbar if you edit your comment. Jan 4, 2023 at 3:42