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

Laplace Transform

  • Thread starter gurtaj
  • Start date
  • #1
20
0
I'm having trouble with this question. Can anyone please guide me.

My Attempt :

= 1/(s-1) * L{t^2*e^-t}
= 1/(s-1) * (2/(s+1)^3)
= 2/((s-1)(s+1)^3))

but that's not the answer , its 2/((s-1) s^3) somehow.
The question is attached below.
 

Attachments

Last edited:

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
I'm having trouble with this question. Can anyone please guide me.

My Attempt :

= 1/(s-1) * L{t^2*e^-t}
= 1/(s-1) * (2/(s+1)^3)
= 2/((s-1)(s+1)^3))

but that's not the answer , its 2/((s-1) s^3) somehow
You are correct: it really is 2/[(s-1)(s+1)^3].
 
  • #3
20
0
But on the test it says its 2/(s^3 *(s-1)), and wolfram alpha confirms it too... The question asked to find F(2).. according to my solution i will get 2/(3^3) which is 2/27 but the answer is 1/4
 
  • #4
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
But on the test it says its 2/(s^3 *(s-1)), and wolfram alpha confirms it too... The question asked to find F(2).. according to my solution i will get 2/(3^3) which is 2/27 but the answer is 1/4
If '*' means multiplication, then your answer is correct (and Maple confirms this). If '*' means 'convolution' then you answer is wrong.
 
  • #5
20
0
In my answer which is 2/((s-1)*(s+1)^3)) , '*' does mean multiplication, so F(2) should be 2/27 , is that correct? ... test got 1/4 however.
 
  • #6
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
In my answer which is 2/((s-1)*(s+1)^3)) , '*' does mean multiplication, so F(2) should be 2/27 , is that correct? ... test got 1/4 however.
I agree with you; if F(s) means the product as given in the question you wrote, then F(2) = 2/27, NOT 1/4. Maybe you wrote the wrong question?

I can see no way to get the answer 2/[(s-1)s^3] using any familiar kinds of operations. A product does not give this, and a convolution also does not give this. You say that Wolfram Alpha gives this; well, I don't believe it. Maple does not give this, and it is essentially equivalent to Mathematica in strength and applicability, so is at least as powerful as Wolfram Alpha (which uses a subset of Mathematica routines). If you say Wolfram Alpha gets this you will need to present exactly what commands you used; perhaps you were solving a different problem without realizing it.
 
  • #7
20
0
This is the exact question... no option of 2/27 :(
 

Attachments

  • #8
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,632
1,268
I'm having trouble with this question. Can anyone please guide me.

My Attempt :

= 1/(s-1) * L{t^2*e^-t}
= 1/(s-1) * (2/(s+1)^3)
= 2/((s-1)(s+1)^3))

but that's not the answer , its 2/((s-1) s^3) somehow
I don't get what you did there.

Pull the exponential in front back inside the integral and then identify the integral as a convolution of two functions. What two functions are they?
 
  • #9
20
0
I'm confused here... are u saying i should put e^t inside integral and do L{e*t^2}?
 
  • #10
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,632
1,268
No, how did you get that? You do realize the integral isn't a Laplace transform, right? When you pull the exponential back in, you get
$$f(t) = \int_0^t \tau^2 e^{t-\tau}\,d\tau.$$ You should recognize the form of that integral.
 
  • #11
20
0
oh wow , i get it now. Thanks you so much for helping.
 
  • #12
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
oh wow , i get it now. Thanks you so much for helping.
You still did not answer my question: you said "Wolfram Alpha gets this too...", and I essentially said I did not believe that claim; I asked you to back it up, by supplying the actual commands you gave to Wolfram Alpha. Please do this; we have tried to help you, now you can try to help us.
 

Related Threads on Laplace Transform

  • Last Post
Replies
5
Views
832
  • Last Post
Replies
3
Views
12K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
612
  • Last Post
2
Replies
41
Views
2K
  • Last Post
Replies
7
Views
941
  • Last Post
Replies
1
Views
505
Top