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Find the inverse Laplace transfor of: a) I' 9 ~12 b) I' ( 6-2)6 c) L' ( (-1)2+4) d) I' ( 21 52+36...

Question

Find the inverse Laplace transfor of: a) I' 9 ~12 b) I' ( 6-2)6 c) L' ( (-1)2+4) d) I' ( 21 52+36

Find the inverse Laplace transfor of: a) I' 9 ~12 b) I' ( 6-2)6 c) L' ( (-1)2+4) d) I' ( 21 52+36



Answers

Determine the inverse Laplace transform of $F.$ $$F(s)=\frac{e^{-s}(s+6)}{s^{2}+9}$$.

Okay. We're trying to ring at T, which is to Teoh. First of all, Teoh, you got two times co sign T in which is

Hello. We have brought the # nine. Indeed we need to find the in royal levels transform of For by a Square -9. Four by Esquire -9. So inverse level is transformation of four by Esquire -9. Waiting to find out. So we have formula that is from the table that if we have any by as Squire minus a Squire then it's inverse level is transformation will be equal to shine 80. Okay but this a square this a and this issue that should be the same. So we have to find a little transformation we have to do. Okay so This is full by has squared -9. We should Right L That is right three By Esquire -3 sq in two. We should be writing for by three as it has to come back to four. Okay now this is constant so we can take constant out. Okay so we'll be reading four x 3. L. universe three by Esquire -3 sq. So this will be collusion 80 four by three. Sign three T. This is inverse. Laplace transformation of the required of the given uh expression.

Hello and Welcome to Probleble 22 of Chapter six. Section 3 you are asked to find the universal posture transform into giving function And this will involve using inverse transform role in personal fractions. Let's get right into this. Uh First I'm going to get a three out of there. So three times at the vest is equal to one over three S squared minus four S plus one. And from here we can factor this to be won over three S -1 Times S -1. Great. And we'll use partial fractions on that. If we left one be equal to a times three s minus one. I'm speeding up the partial fractions because I assume knowledge of it uh Plus B times x minus one. Well what happens when B is equal when s is equal to one will have one equal to a times three minus +12. So is able to have and be what happens when s is equal to one third will have one is equal to be time one third minus one which is negative two thirds be times negative two thirds. That's three over negative to be Equals -3/2. Great. And we can plug this right into what we had up there. We'll have three times f. S. Is equal to well half from the egg. Um Yes We'll have 1/2 times one over X -1 plus. Uh Let's do a minus minus three halves. Times one over three S -1. and from here we can divide by three because it's back to being simple. So Cross out that three make this into a six. It will also cross that three and make that in today one. Okay, now, from the inverse transform rule, we can pretty easily take the universal cost transform of this and therefore F f T Will be equal to 1/6. Eat the T. Be more careful with the second part. Remember there's a three S there. So really this we can factor that 32 out there and we were left with s minus one third, which is a a completely different answer than um Just leaving the three in there. But this will be a minus 1/6 because we're factoring with that three And it will be E to the T over three. And that is the solution to this in verse plus transport.


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