• Support PF! Buy your school textbooks, materials and every day products Here!

The second shifting theorem and the unit step function

  • Thread starter Rubik
  • Start date
  • #1
97
0

Homework Statement



I am trying to do some revision for an upcoming exam and one question I am trying to figure out is

Use the second shifting theorem to find the Laplace transfrom of the following function:
f(t) = t2, t < 4
t, t ≥ 4

Homework Equations





The Attempt at a Solution


I just don't understand how to get from the question to
f(t) = t2[1 - u(t-4)] + tu(t-4)
I am really struggling with applying the second shifting theorem to express in terms of the unit step function I am failing to see how it works because nothing is explained in basic detail?
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,519
734

Homework Statement



I am trying to do some revision for an upcoming exam and one question I am trying to figure out is

Use the second shifting theorem to find the Laplace transfrom of the following function:
f(t) = t2, t < 4
t, t ≥ 4

Homework Equations





The Attempt at a Solution


I just don't understand how to get from the question to
f(t) = t2[1 - u(t-4)] + tu(t-4)
I am really struggling with applying the second shifting theorem to express in terms of the unit step function I am failing to see how it works because nothing is explained in basic detail?
Think of it this way. You start out with f(t) = t2. Then at t = 4 you want to take out the t2 and put in t, so you add the term u(t-4)(-t2+t).

Then put it all together:

f(t) = t2+u(t-4)(-t2+t)

Now, if you wish, you can collect terms on the various powers of t:

f(t) = t2(1-u(t-4)) + tu(t-4)
 

Related Threads for: The second shifting theorem and the unit step function

  • Last Post
Replies
8
Views
923
  • Last Post
Replies
1
Views
847
  • Last Post
Replies
1
Views
823
Replies
4
Views
4K
  • Last Post
Replies
3
Views
18K
Replies
5
Views
4K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
1
Views
8K
Top