Laplace transform - step function

  • Thread starter Pi Face
  • Start date
  • #1
76
0

Homework Statement


f(t)= 1 if 0≤t≤1 ; 0 is t>1
find the laplace transform


Homework Equations





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
 

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
15,131
1,725
[I know I have to shift it and get
u_a(t)=u(t-a)= 1 if 0≤t≤a, 0 if a>1
What?
 
  • #3
76
0
I thought there was a step involving replacing the discontinuous point with a
 
  • #4
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
15,131
1,725
There is, but your description doesn't make sense. When is ua(t) equal to 0 and when is it equal to 1?
 
  • #5
76
0
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
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
15,131
1,725
I'm not following what you're getting at. Replace what 1 with a?
 
  • #7
76
0
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
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
15,131
1,725
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.
$$u_1(t) = u(t-1) = \begin{cases}
0 & t<1 \\
1 & t\ge 1
\end{cases}$$
 

Related Threads on Laplace transform - step function

  • Last Post
Replies
1
Views
13K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
621
Replies
5
Views
7K
  • Last Post
Replies
3
Views
5K
Replies
4
Views
5K
  • Last Post
Replies
9
Views
1K
Top