What is Inverse laplace transform: Definition and 165 Discussions
In mathematics, the inverse Laplace transform of a function F(s) is the piecewise-continuous and exponentially-restricted real function f(t) which has the property:
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{\displaystyle {\mathcal {L}}\{f\}(s)={\mathcal {L}}\{f(t)\}(s)=F(s),}
where
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{\displaystyle {\mathcal {L}}}
denotes the Laplace transform.
It can be proven that, if a function F(s) has the inverse Laplace transform f(t), then f(t) is uniquely determined (considering functions which differ from each other only on a point set having Lebesgue measure zero as the same). This result was first proven by Mathias Lerch in 1903 and is known as Lerch's theorem.The Laplace transform and the inverse Laplace transform together have a number of properties that make them useful for analysing linear dynamical systems.
Gents,
I have this problem:
find the inverse laplace transfor for
Y1(s) = exp(-s)/s^2
Y2(s) = {1/[4*(s+1)]}*exp(-2*s)
my solution is:
using the 2nd shifting theroem
y1(t) = (t-1) H(t-1)
y2(t) = (1/4)*exp(2-t)*H(t-2)
Is my solution correct?
I am trying to find the inverse LaPlace transform of
F(s)=\frac{2s+12}{s^2+6s+2\sqrt{2}}
Using partial fraction decomposition on the above rational expression seems tedious. Is there any other method?
Thanks
My book on signal processing says that:
f(t) = \frac{1}{2\pi j} \int_{c-j\infty}^{c+j\infty} F(s) e^{st} ds = \lim_{\Delta s \to 0} \sum_{n = -\infty}^{\infty} \Big[ \frac{F(n\Delta s)\Delta s}{2\pi j} \Big] e^{n\Delta s t}
I don't get this. How/Why can you write a integration over a...
Homework Statement
1/s^5
Homework Equations
I was thinking I need to use n!/s^n+1
The Attempt at a Solution
But n would then be 4, so n! will be 24. Not sure what to do?
Hi I'm having problems find the inverse Laplace transform of \frac{s}{{\left( {s + 4} \right)^4 }} via a table/look up method.
In another question part I found the inverse Laplace transform of (s+4)^-4 by considering \frac{{d^3 }}{{db^3 }}\left[ {\left( {s + b} \right)^{ - 1} } \right] so...
Hi How would I find the inverse laplace transform of this?
I(s) = \left( \frac{1}{s(1+e^{-s})}\right) \left( \frac{1}{Ls+R}\right)
i(t)=?
L, R are constants. I recognize the first term to be a geometric progression (square-wave function). With an infinite number of terms in that...
Hello everyone,
i have this question and not even sure how to approach it:
\frac {di}{dt}+4i+3\int_{0^-}^t{i(z)dz = 12(t-1)u(t-1)
and i(0^-) = 0
find i(t)
last topics we covered were laplace transforms (and inverse) and dirac delta function.
At least some hint to get me started...
Hi - I really need someone to show me step by step how to do an Inverse Laplace transform using a contour integral. The one I would like to understand is the frequency function 1/sqrt(s)
Thank you if you can help me out.
Steve
I am asked to find the inverse laplace transform of the following function:
\frac{ \left( s+3 \right) }{ \left( s+1 \right) \left( s+2 \right) }
Using tables, can anyone help me understand why the answer is:
2e^{-t} - e^{-2t}
I'm completely loss on this one, and yet the book...
Can somebody help me to find the inverse laplace transform of these functions
exp(sqrt(1+s))
sqrt(1+s))
I tried solving these using MATLAB and mathematica,it is unable to give a result.
Do they contain any closed form solution or should i have to go for a numerical technique to solve...
Having difficulty finding the inverse laplace transform!
Hello everyone, I am really stuck on finding the inverse Laplace transform for this:
f(s)=\frac{5se^{-3s} - e^{-3s}}{s^{2}-4s+17}
Heres my reasoning: I feel that I should rewrite the denominator in some kind of form such as (s-2)^2...
Hi I am currently working my way through a control systems textbook and I am bringing my understanding of the relevant mathematics up to speed. I have happened across the Laplace Transform which I am happy enough with. I am concerned however that given the fact that this is a real project I may...