# Laplace transform - step function

1. Feb 9, 2012

### Pi Face

1. The problem statement, all variables and given/known data
f(t)= 1 if 0≤t≤1 ; 0 is t>1
find the laplace transform

2. Relevant equations

3. The attempt at a solution
I know u(t)= 0 for t<0 and 1 for t≥0

I know I have to shift it and get
u_a(t)=u(t-a)= 1 if 0≤t≤a, 0 if a>1

am I even going the right way?
then I think I integrate it from 0 to inf with
∫e^(-st)u_a(t) dt = ?

not sure what to do from here

2. Feb 9, 2012

### vela

Staff Emeritus
What?

3. Feb 9, 2012

### Pi Face

I thought there was a step involving replacing the discontinuous point with a

4. Feb 9, 2012

### vela

Staff Emeritus
There is, but your description doesn't make sense. When is ua(t) equal to 0 and when is it equal to 1?

5. Feb 9, 2012

### Pi Face

f(t) is 0 when t>1 and 1 when it is between 0 and 1, inclusive.

so for ua(t) wouldnt I just replace the 1 with a?

6. Feb 9, 2012

### vela

Staff Emeritus
I'm not following what you're getting at. Replace what 1 with a?

7. Feb 9, 2012

### Pi Face

You replace the discontinuous point with a right? Which happens to be one in this problem because it has a value of 0 whe greater than 1 and a value of 1 when between 0 and 1. So the discontinuous point would be at 1? Which you replace with a?

8. Feb 9, 2012

### vela

Staff Emeritus
You have it backwards. You don't replace 1 with a. You set a to 1, i.e., u1(t) = u(t-1). That's the step function shifted to the right by 1.
$$u_1(t) = u(t-1) = \begin{cases} 0 & t<1 \\ 1 & t\ge 1 \end{cases}$$