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IIl etisalat12.18 AM7 37%webwork aurakac aeAssignment8: Problem 8Previous ProblemProblem ListNext Problem3 points) Find the Laplace transform F(s) = L {f(t)} of the...

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IIl etisalat12.18 AM7 37%webwork aurakac aeAssignment8: Problem 8Previous ProblemProblem ListNext Problem3 points) Find the Laplace transform F(s) = L {f(t)} of the function f(t) = e2-12h(t - 6) , defined on the interval t2 0.F(s) = L e2-12h(t _ 6)}help(formulas)Preview My AnswersSubmit AnswersYou have attempted this problem 0 times: You have unlimited attempts remaining:Email instructorPage generated at 12/18/2018 at 03.24pm EST

IIl etisalat 12.18 AM 7 37% webwork aurakac ae Assignment8: Problem 8 Previous Problem Problem List Next Problem 3 points) Find the Laplace transform F(s) = L {f(t)} of the function f(t) = e2-12h(t - 6) , defined on the interval t2 0. F(s) = L e2-12h(t _ 6)} help (formulas) Preview My Answers Submit Answers You have attempted this problem 0 times: You have unlimited attempts remaining: Email instructor Page generated at 12/18/2018 at 03.24pm EST



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Use the results of Problem 19 to find the inverse Laplace transform of the given function. $$ F(s)=\frac{1}{9 s^{2}-12 s+3} $$

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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