That's a fair point. I guess in electronics you can derive a transfer equation when you input a sinusoid into the circuit, but quantum mechanics isn't exactly similar in that way
Isnt that curious? Idk i find it strange.
Maybe it works in circuits because everything is linearized as you said, but in quantum mechanics for instance would this fall apart? Its been so long since i took qm so i probably dont remember well enough to generate an example like that
This is an interesting comment. I'm not sure how to take it further, but maybe it is an explaination?
Something else I was thinking about (which may be complete nonsense) is that -sin^2 is equal to cos^2 when looking at phase and magnitude ONLY. The dc bias separates them, but working with j...
Hey haushofer, ya i tried that. if you do that then it just spits it back out. jsinx = jsinx.
I understand all of this, ill stop using the word "works" since that seems to be what we are hung up on.
Mathematically, if you input a sin signal into a circuit, calculate the transfer...
Using phasors to derive the magnitude of the transfer function of a circuit gives THE EXACT SAME results as substituting jsin=cos. Thats what i mean by work. Input output. If you want to argue what word to use for that instead of WORKS thats fine
Hutchphd had what seemed to be the only helpful...
I really appreciate all the posts but this is the only one that is attempting to answer my question. Is this expandable?
It is interesting to think about and i enjoy it. Why do people post things like this lol. The only reasonable responses should be:
i dont know
it is unknowable
this is...
But you need the derivative of apples to be monkeys, as well as orthogonal. So i dont see the point you are making.
Yes it does? Substitute cos(wt) with j*sin(wt) and thats exactly what you get, and kinda my entire point here.
I get it, I understand phasors, i am an MSEE working in industry as an analog designer. Just asking for an example where that substitution doesnt work thats it. Phasors are already abstract, and its mysterious to me as to why that substitution seems to always work.
Does that complex exponential equation show that i*sin = cos
I am just wondering why it seems to always work, i cant find an example where it doesnt. But then also, i cant prove i*sin = cos.
Without every invoking complex exponentials, eulers formula, etc. Why can i simply replace all cos...
another example:
i have a transfer function given by the complex number (A+jB). I multiply my input sin(wt) and i get Asin(wt)+jBsin(wt). Using the equality above, it becomes Asin(wt) + Bcos(wt), which is just standard form of any sinusoid with a magnitude of sqrt(A^2 + B^2). No need to convert...