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

1. John_henderson

Hi guys, im new to this topic i would appreciate it if someone can show me in how to proceed forward with this problem.

2. TuringTest

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

3. John_henderson

Thanks that site looks useful

4. John_henderson

The examples on the website are kinda difficult to understand, im still kinda confused....?

5. TuringTest

do you know the $\mathcal L\{u_c(t)f(t-c)\}=e^{-cs}F(s)$transform?

6. John_henderson

Yes i know the forumla but dont know how to apply it yet... Im i suppose to sub in the interval values in first.

7. TuringTest

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$f(t)=t-tu_1(t)$so far so good?

8. John_henderson

why is f(t)= 0 ? is that from the limits 0<t<1

9. TuringTest

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

10. John_henderson

yes thats correct, But why?

11. TuringTest

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$f(t)=t-tu_1(t)$satisfies the first two parts of the step function?

12. John_henderson

Oh right i see, so do i integrate now?

13. TuringTest

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)

14. John_henderson

H(t-a) ?

15. TuringTest

but the all-important question is"what is a ?".

16. John_henderson

1 i guess?

17. John_henderson

well is it?

18. John_henderson

lol im so confused at the moment, im totally new to this!

19. TuringTest

no, you need to understand the heavyside function for H(t-1) what is the value when t=2 ?

20. John_henderson

0

21. John_henderson

i mean 1 ?