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My understanding is that the Laplace transform evaluated at $s = i \omega t$ can be used to evaluate the steady-state of a function. How is this done? I can't find any information on this in my textbooks nor on the internet.

Thanks in advance.

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    @JonaGik: the other question states "[...] and, when we're concerned with the steady-state response, it equals (omega*i)." This looks rather duplicate to me -> either you should take out this part of the question in the other thread or the answers should be merged. In any way, I would urge you to try at another SE.2012-03-23

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Let $f(t)$ denote the time-domain function, and $F(s)$ denote its Laplace transform. The final value theorem states that: $ \lim_{t \to \infty} f(t) = \lim_{s\to 0} sF(s), $ where the LHS is the steady state of $f(t).$ Since it is typically hard to solve for $f(t)$ directly, it is much easier to study the RHS where, for example, ODEs become polynomials or rational functions in $s.$

You can get more info in course notes like this one: PDF, or in control engineering/system theory books such as Kailath: Linear Systems or Ogata: Modern Control Engineering.

Also, as noted in the comments, there are Physics Stackexchange and Electrical Engineering Stackexchange