Question

Express the following in terms of Heavyside Function=> H(t-a) and find its laplace transform Where
F(t) = t 02

Answer 1

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

Answer 2

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

Answer 3

Thanks that site looks useful

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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?

Answer 8

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

Answer 9

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

Answer 10

yes thats correct, But why?

Answer 11

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?

Answer 12

Oh right i see, so do i integrate now?

Answer 13

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)

Answer 14

H(t-a) ?

Answer 15

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

Answer 16

1 i guess?

Answer 17

well is it?

Answer 18

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

Answer 19

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

Answer 20

0

Answer 21

i mean 1 ?