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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
 one year ago
 one year 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
 one year ago
 one year ago

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

TuringTestBest ResponseYou've already chosen the best response.0
It'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
 one year ago

John_hendersonBest ResponseYou've already chosen the best response.0
Thanks that site looks useful
 one year ago

John_hendersonBest ResponseYou've already chosen the best response.0
The examples on the website are kinda difficult to understand, im still kinda confused....?
 one year ago

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

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

TuringTestBest ResponseYou've already chosen the best response.0
For 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?
 one year ago

John_hendersonBest ResponseYou've already chosen the best response.0
why is f(t)= 0 ? is that from the limits 0<t<1
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
your 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
 one year ago

John_hendersonBest ResponseYou've already chosen the best response.0
yes thats correct, But why?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
you 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?
 one year ago

John_hendersonBest ResponseYou've already chosen the best response.0
Oh right i see, so do i integrate now?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
Well 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)
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
but the allimportant question is"what is a ?".
 one year ago

John_hendersonBest ResponseYou've already chosen the best response.0
lol im so confused at the moment, im totally new to this!
 one year ago

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