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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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    possible duplicate of [Frequency Response of Circuits - Laplace Transforms](http://math.stackexchange.com/questions/120672/frequency-response-of-circuits-laplace-transforms)2012-03-22
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    I still believe the question might be better off in the physics or electrical engeneering stack exchange.2012-03-22
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    It just becomes a Fourier transform.2012-03-22
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    A 1965 book is Murry Spiegel, Shaum's Outline of *Theory and Problems of Laplace Transforms*, McGraw-Hill.2012-03-22
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    The Laplace transform can be used to evaluate the transient response of an electrical circuit when an input voltage is applied to it; or the behavior of a mechanical beam when is subjected to a load applied to it. Both situations can be modeled by differential equations, depending on the initial conditions. These are solved using the Laplace transform and afterwards the inverse transform is used to find the result.2012-03-22
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    @Fabian - to some extent it is a duplicate but this question is more clear, I believe, but I would ideally like the other to stand independently in addition.2012-03-23
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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