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I never had the concept, but I found this video on Youtube. http://www.youtube.com/watch?v=-e0ITPJEYJI They seem to be saying is if the delayed input is the same as the output delayed then it's time invariant, I think.
You know what? This course looks like it was created by the instructor and it's sole purpose is to act as a "weed killer". It removes people from the possible graduating class.
I have a trick for you. If you can take any math courses continuing ED or ones that are taught my a non math professor. Typically these are taught by engineers and a lot of the proofs of theory etc is minimized.
@KISS: You are correct in saying that taking some courses from non-math instructors is a good idea. But the instructor under discussion is not a weed killer per se. But the way he is going, he will definitely kill some of the weed alongside the non-weed. Simply, he does not know anything about the subject. He googles things up and writes them down on a sheet of paper and comes to the class for lecturing. I don't know why he is not following the prescribed textbook. But I have been continuously telling him that he shouldn't deal the topics in random order because it is confusing all the students.
Now I have put the Q1 in proper setting and you can also see the book's explanation. Thanks.
I could not agree more. I'm having a hard time, especially tonight (medical issue) wrapping by head around the mathematics. Intuitively, though I think I can make some intuitive sense out of some of it.
Taking a really simple example of an amplifier with a gain of 10. No matter where in time you apply the input signal (say a sin wave) it will have the same output, so it;s time invariant.
Remember that funky function called u(t) or the unit forcing function that was probably around in the Lalpace Transform stuff? Same deal, in most of the cases, the system has the same response no matter when the stimulus is applied. Your delaying the application of the signal, NOT applying the signal after a delay. I think that's important.
Now if you has s(t) representing the path of some bug on an airplane propeller and at t=0 you pushed the propeller, the bug can be anywhere, so it's time variant.
The instructor doesn't necessarily have to be the weed killer, it could very well be the topic. "Introduction to Discrete Mathematics" and "Dynamics" were two of those courses and no where near subjects like Physics I (basically materials) or Physics II ( Electricity and Magnetism) and Physics II (Relativity). The point is the engineer will teach the math courses from a practical standpoint. The Electrical Engineer might never see this stuff, so the engineer won't think it's that important.
Sorry, but I like to come back to Q2.
For my opinion, the text - together with the drawing - as quoted in post#1 - is somewhat confusing (primarily because of the drawing with two equal looking batteries), however it is correct because the text says V2=-V1.
But there is one single error in the second part (shown with post#4) - and that can be found in the drawing at the bottom (right side). Again, the polarity of the battery in the drawing is somewhat confusing but in conjunction with the text (V2=-V1) it seems to be (more or less) OK, but very uncommon. However, the information I1=I2 certainly is not correct. It should be only I2 (very low, according to the text).
Additional remark: Of course, it is not an "additive system" because it contains a non-linear element (diode) with a non-linear voltage-current relationship. Thus, the superposition theorem may not be applied.
in your first problem, in simple words the time invariant system is the system which its "manner" of response remains the same. here this manner is noted Y1. in your example, it is shown that in different time points, the response remains in the same form Y1, of course depends on the instant when the output is measured.