# inverse laplace

#### full

Joined May 3, 2014
225
hello
inverse laplace transform
how can do invert the laplace for this example?

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#### WBahn

Joined Mar 31, 2012
26,398
Well, what do you know about the order of the numerator and denominator in order to use the tables?

#### full

Joined May 3, 2014
225

#### WBahn

Joined Mar 31, 2012
26,398
In order to use partial fractions, you have to start with a proper fraction.

So just as (x/y) is an improper fraction unless y>x, so too is a polynomial fraction improper unless the order of the denominator is greater than the order of the numerator. You deal with it the same way, too. You divide the denominator into the numerator and get a whole part plus a fractional part, just as (5/3) can be rewritten as (1)+(2/3).

#### MrAl

Joined Jun 17, 2014
8,231
Hello there,

Another interesting venture would be to change that "26" in the denominator to a "25", which allows the denominator to be factorized with reals so you can 'try' partial fractions the way you are probably used to doing so far (that's not to say that you can or can not factor it already, but it may help anyway).

#### t_n_k

Joined Mar 6, 2009
5,455
Hello there,

Another interesting venture would be to change that "26" in the denominator to a "25", which allows the denominator to be factorized with reals so you can 'try' partial fractions the way you are probably used to doing so far (that's not to say that you can or can not factor it already, but it may help anyway).
Interesting idea. However, I believe the problem of numerator order remains. One must do the long division or its equivalent to obtain workable forms.
The inverse transform result includes the delta function.

#### MrAl

Joined Jun 17, 2014
8,231
Hi,

He he, that's what i thought would happen but i didnt want to give out any more hints just yet
I didnt try long division though, maybe you can try that and post results eventually.
I just used another trick involving known Laplace operations, i dont want to give that away just yet.

Thanks for confirming this though. The OP will have to work on this next and it will be interesting to see what the OP comes up with.

#### WBahn

Joined Mar 31, 2012
26,398
Hello there,

Another interesting venture would be to change that "26" in the denominator to a "25", which allows the denominator to be factorized with reals so you can 'try' partial fractions the way you are probably used to doing so far (that's not to say that you can or can not factor it already, but it may help anyway).
The fact that the denominator has complex conjugate roots doesn't cause problems and partial fractions works just fine as far as that's concerned. The problem is that it is not a proper polynomial fraction.

#### MrAl

Joined Jun 17, 2014
8,231
The fact that the denominator has complex conjugate roots doesn't cause problems and partial fractions works just fine as far as that's concerned. The problem is that it is not a proper polynomial fraction.
Hello again,

Yes i am aware of that, but you'll note that one of the OP's complaints was that he could not use partial fractions, and i believe that was because he wasnt able to 'factor' the denominator because it requires a complex factorization, and he obviously never encountered that scenario before this. So with real roots he could at least make a little progress the way he normally does it, most likely. But eventually he'll have to do it with complex roots too. It's easy to change the form of the equation to make it proper as there are several ways to handle that, but i didnt want to give that information out just yet
I guess now the OP knows the 'fraction' is improper and has to find a way to fix that first. It's probably a good lesson.

Since it was also given out now that the solution includes an impulse, i think it would be interesting to look at this function in a circuit to see how it behaves with and without that impulse because it is tempting to leave out the impulse part.

#### full

Joined May 3, 2014
225
my solution

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#### djsfantasi

Joined Apr 11, 2010
7,688

#### full

Joined May 3, 2014
225

#### djsfantasi

Joined Apr 11, 2010
7,688

#### full

Joined May 3, 2014
225
obs!
yes , I have wrong in division is -6s not -10s ,sorry ...

#### djsfantasi

Joined Apr 11, 2010
7,688
No smart reply by me intended. And no apology needed. I was curious what your math looked like using -6s?

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