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1. Find the Laplace transform of flt)= sin? 2t 2. Find the Laplace transform of flt)= t4 cosh t...

Question

1. Find the Laplace transform of flt)= sin? 2t 2. Find the Laplace transform of flt)= t4 cosh t

1. Find the Laplace transform of flt)= sin? 2t 2. Find the Laplace transform of flt)= t4 cosh t



Answers

Determine the Laplace transform of the given function $f.$ $$f(t)=e^{-2(t-1)} \sin 3(t-1) u_{1}(t)$$.

Five you are today. We are going to sort problem number 25 in this leader to find the LaPlace transform off into the Bola do de in Goa weren minus saying square. Okay, one minus saints. Cloherty can better done us both. Where? Okay, it is a control. Work less Goethe. Droopy. Who are they are by so love Plus transform off. You know the Bader Burundi and go. We're blessed close to bay. Words are back. Flu lamp lesson for Wolf. You know the bar Fruity. Did you know Banco plus Leper? Essential off Here is the duty in the course today. Oh, don't bite. We're just gonna go line but do in tow s minus two. He is to do the lamp. Isn't one best menace to love Lapland Stencil off Costea Close to be Is I asked my in squared plus little square. So when I am president some years to duty wants to be back through is land I do Indo Yes minus two. They were by Yes might have through the whole square plus four. There's their duffel question. Thank you

Hello and welcome the problem. 10 Chapter six Section 3 here were asked to final applause transformation of the given heavy said function. Have you said functions. And um to do this we have to remember the golden rule of each little past transformations and that's that you subsea of T um times F of t minus C is equal to E. To the minus C. S. Times little plus transformation of um F. Of T. All right that is. And of course the left side is a little pot transformation as well. So with this we can just substitute this F. F. T minus C. For one because that's essentially what all of these are being multiplied by. So doing that we're gonna be left with E. To the minus s. Well what's a little past transformation of one? What's one of us? Because the plus transformation T. To the end that we found in previous sections is in factorial Over us to the end plus one. So plugging this in The zero factorial is one over S. To the zero plus one is one. Yes. So I left with one of our S. And well so the whole posture information of you won each of the negative s over us. Likewise we can repeat this process for the others. We get to E. To the minus three S over us And -6 e. to the -4 s. Over us. We can of course combine them to be E. To the minus S. Plus two E. To the minus three S. Find a six e. to the -4 s over S. and that concludes the problem.

Hello and welcome to problem 10 of chapter six. Section three you are asked to find the applause transform of the given function F. T. Where's the linear combination of use of one. Use of three and use it for. So let's get into this. We're going to use the equation we learned at the beginning of this chapter. Which is which is that use of C. T. F. Of T minus C. Is equal to the universal applause transform of E. To the minus C. S. Times F. Of S. Great. And how does that help us? Uh Well what is multiplied by this use of one in this case? Um Actually it's uh in this case it's one in this case it's to this case it's six so we can really sub substitute that in. And um what is the laplace transform of 12 and three? Well it's that constant over S. So it will be one over S. To over s. -6 arrests. So let's let's find out what the final laplace transformation is going to be a capital F. Of S. Well that's gonna be eat the minus S over S. And we'll see argument of linear combination with a plus Uh to E. to the -3 s. and -6 E. To the minus for us for this S right there. And that concludes our problem


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