I think im being stupid but why can i not use a partial fraction in this question instead of compleating the square
#Inverse Laplace Transform
prisma hazel
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I think im being stupid but why can i not use a partial fraction in this questio...
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fast pier
yeah i get it to (s-1)(s+7)
and then do partial fraction decomp^^
But yeah i dont get why either
prisma hazel
thats what i did but you get nothing like what they got
fast pier
🤔
there is a invers laplace calculator
let me put in the expression and see what it says
prisma hazel
i beieve there may be some sort of a trick question as it was 8 marks
so theres probably a little thing i have to look out for but not sure what that would be
fast pier
yeah
@prisma hazel did you try the way we both "think" is "right"?
what did u get A and B too?
prisma hazel
the partial fraction cancels out so you end up with the inverse laplace of 1/(s+7)
which gives e^-7t
prisma hazel
i was thinking it may be due to the numerator but im not too sure
fast pier
Yeah thats not a bad idea
I cant help you any further sadly since i've gtg
but in my course we didnt use those cosh and sinh
we just did it the way we both did
prisma hazel
no youre alright, makes me happier knowing that its not just me lost lol
fast pier
😆
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I think im being stupid but why can i not use a partial fraction in this questio...
You can. It's just another approach.
prisma hazel
it comes out with a compleatly different answer tho
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it comes out with a compleatly different answer tho
Hm. What did you get?
prisma hazel
e^-7t
pine mirage
Oh! I recently learnt this in University. Laplace transforms, derivative operator and Euler-Cachy diferential equations
prisma hazel
Yeah, that's the same thing.
ahhhhh i assume its to do with this
not sure why they would make it so complicated then
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ahhhhh i assume its to do with this
Yes.
cosh(x) = (e^x + e^(-x))/2
sinh(x) = (e^x - e^(-x))/2
So:
e^x = cosh(x) + sinh(x)
e^(-x) = cosh(x) - sinh(x)
Not sure why they did it like that, but that's still a valid approach.
pine mirage
Not sure why they did it like that, but that's still a valid approach.
I think it's because whoever wrote the answer was solving it based on the Laplace Transform table
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I think it's because whoever wrote the answer was solving it based on the Laplac...
Well, yes, but you usually just use partial fractions, then use the table.
Oh, right. I can share my table.
pine mirage
Well, yes, but you usually just use partial fractions, then use the table.
Yep that's right!
pine mirage
Oh, right. I can share my table.
Ok. I have my demonstrations of the Laplace transforms that I used most of the times
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Here you go.
The words at the top are "original" and "image".
I have a table of properties, too, but there would be too much to translate.
prisma hazel
i am given this table in the exam
feels like the partial fraction route is so much easier
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I see. We didn't have an exam for it.
prisma hazel
but i assume they mainly want us try it with completing the square
not sure why
but thats university for you
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Nah. I think you can use whatever approach works, really.
I can translate my table of properties if you want.
There are quite a lot of them there.
prisma hazel
no thats alright we arent expected to use anything more than we have
but thanks anyway
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Oh, alright. You're welcome!
If you do want to see it, DM me. Shouldn't take me too long to translate.
neat gyro