## John_henderson Group Title 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 one year ago one year ago

1. John_henderson Group Title

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 Group Title

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 Group Title

Thanks that site looks useful

4. John_henderson Group Title

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

5. TuringTest Group Title

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

6. John_henderson Group Title

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 Group Title

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 Group Title

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

9. TuringTest Group Title

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 Group Title

yes thats correct, But why?

11. TuringTest Group Title

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 Group Title

Oh right i see, so do i integrate now?

13. TuringTest Group Title

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 Group Title

H(t-a) ?

15. TuringTest Group Title

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

16. John_henderson Group Title

1 i guess?

17. John_henderson Group Title

well is it?

18. John_henderson Group Title

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

19. TuringTest Group Title

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

20. John_henderson Group Title

0

21. John_henderson Group Title

i mean 1 ?