How to Find the Inverse Laplace Transform for a Given Function?

Click For Summary

Homework Help Overview

The discussion revolves around finding the inverse Laplace transform of a given function, specifically F(s) = s / ((s+a)^2 + w^2) and its corrected form with an additional power n in the denominator. The subject area is Laplace transforms within the context of differential equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the steps needed to derive the inverse Laplace transform and are questioning the notation and components of the function, particularly the presence of the variable k and the power n in the denominator.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the function and its components. Some guidance has been offered regarding the notation, but there is no explicit consensus on the correctness of the original function or the final answer provided.

Contextual Notes

There is a noted discrepancy in the function provided by the original poster, leading to questions about the validity of the transform and the final answer. Participants are also considering the implications of the power n on the inverse transform process.

mr.engineer
Messages
2
Reaction score
0
""Invers laplace transformation""

Homework Statement



Find invers laplace transform f(t) for F(s)= s /((s+a)^2 +w^2)) ?


Homework Equations





The Attempt at a Solution



i have the final answer but i need the steps to know how i can do it exactly
the final answer is :
f(t) = t^k sin(wt) e^-at
 
Physics news on Phys.org


I am curious where the k comes from. It is not in your transform.
 


yeah your notation is good,i there is something missing in my function
the true function is F(s)= s/((s+a)^2+w^2)^n , there is power n on the denominator.
t^k is just the power of t term causes by n maybe its the same gap with me..
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K