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 2 years ago
Express the following in terms of Heavyside Function=> H(ta) and find its laplace transform Where
F(t) = t 0<t<1
0 1<t< 2
1 t>2
 2 years ago
Express the following in terms of Heavyside Function=> H(ta) and find its laplace transform Where F(t) = t 0<t<1 0 1<t< 2 1 t>2

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John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0Hi guys, im new to this topic i would appreciate it if someone can show me in how to proceed forward with this problem.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0It's been a while since I've done this, but here's what I'd work from: http://tutorial.math.lamar.edu/Classes/DE/StepFunctions.aspx

John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks that site looks useful

John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0The examples on the website are kinda difficult to understand, im still kinda confused....?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0do you know the \[\mathcal L\{u_c(t)f(tc)\}=e^{cs}F(s)\]transform?

John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0Yes i know the forumla but dont know how to apply it yet... Im i suppose to sub in the interval values in first.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0For 0<t<1 we have f(t)=t, so let's start with that Now, since for 1<t<2 we have f(t)=0 we need to subtract the t we had at the beginning, and we need to initiate that using the step function with c=1. So, so far that gives us\[f(t)=ttu_1(t)\]so far so good?

John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0why is f(t)= 0 ? is that from the limits 0<t<1

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0your step function is\[f(t)=\left\{\begin{matrix}t&&0<t<1\\0&&1<t<2\\1&&t>2\end{matrix}\right.\]correct? if so, then for t between 1 and 2 your function should equal zero

John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0yes thats correct, But why?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0you asked why f(t)=0 for 1<t<2... that's why; it's stated in your step function (sorry for the slow replies, my connection is horrible right now) so do you see how\[f(t)=ttu_1(t)\]satisfies the first two parts of the step function?

John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0Oh right i see, so do i integrate now?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0Well first off, I am thinking you want the laplace transforms, not regular integration. We need to do some more manipulation before we can do that. Secondly, we have not yet added the part that will make it such that f(t)=1 for t>2 any ideas how you might do that? (hint: it requires adding a single term, which is another step function)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0but the allimportant question is"what is a ?".

John_henderson
 2 years ago
Best ResponseYou've already chosen the best response.0lol im so confused at the moment, im totally new to this!

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0no, you need to understand the heavyside function for H(t1) what is the value when t=2 ?
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