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Find inverse LaPlace transform - partial fractions
- Thread starter linhvn
- Start date
Hi,
Didn't you ask this question in the other thread?
Once you get the partial fraction decomposition, you then use a table to do the inverse Laplace.
Since we are on this subject and we looked at this in the other thread, the last solution I gave would be more useful than solving using that form you show here. That's because Transform tables usually show transforms for expanded factors not individual factors.
For example, if you have a factor:
s^2+10000
you don't have to break it down into:
(s-100*j)*(s+100*j)
you just have to look up a transform with "s^2+a" in the denominator with 'a'=10000 and you should find the transform for that.
For example:
A*w/(s^2+w^2) <=> A*sin(w*t) u(t)
but if you broke that down into parts it would be:
A*w/((s+j*w)*(s-j*w))
and then the inverse transform:
(j*e^(-j*t*w)*A)/2-(j*e^(j*t*w)*A)/2
which is not as straightforward.
The s^2+a*s+b factor may be a little harder to transform but same idea.
Whatever you do you should do it the way you are most comfortable with.
Didn't you ask this question in the other thread?
Once you get the partial fraction decomposition, you then use a table to do the inverse Laplace.
Since we are on this subject and we looked at this in the other thread, the last solution I gave would be more useful than solving using that form you show here. That's because Transform tables usually show transforms for expanded factors not individual factors.
For example, if you have a factor:
s^2+10000
you don't have to break it down into:
(s-100*j)*(s+100*j)
you just have to look up a transform with "s^2+a" in the denominator with 'a'=10000 and you should find the transform for that.
For example:
A*w/(s^2+w^2) <=> A*sin(w*t) u(t)
but if you broke that down into parts it would be:
A*w/((s+j*w)*(s-j*w))
and then the inverse transform:
(j*e^(-j*t*w)*A)/2-(j*e^(j*t*w)*A)/2
which is not as straightforward.
The s^2+a*s+b factor may be a little harder to transform but same idea.
Whatever you do you should do it the way you are most comfortable with.
I did this with algebraic method and find it easy.
Oh ok that's great.
Hello again,
I forgot to mention that I rarely do this anymore by hand I use math software. It's much faster and then I get to concentrate more on the original problem rather than how to do the transforms and inverse transforms. It's good to know how to do it by hand too though.
I forgot to mention that I rarely do this anymore by hand I use math software. It's much faster and then I get to concentrate more on the original problem rather than how to do the transforms and inverse transforms. It's good to know how to do it by hand too though.
I have got this battery , speed indicator of my electrical motorbike but I cannot find the datasheet in the internet, this is made in China. Can you help me know the function of DD, 1, 2, 4/6, 3 , Yxt Sd pins?
I have not seen that board before. You should start a new thread for this though this thread was for theoretical electrical problems of a specific nature.
sr, wrong place, btw could you tell me which pins ( colored wire) is speed signal? this is indicator of electrical motor.
Hi,
I don't know because I've never seen that board before and it does not turn up on a search so far.
The best I can think of at the moment is that you should try to measure the pins with a scope to try to figure it out, if the board is still working that is.
