What is the Laplace Transform of f(x)=e^{bx}.sin ax?

Click For Summary

Discussion Overview

The discussion revolves around finding the Laplace Transform of the function f(x) = e^{bx} sin(ax). Participants explore different methods and approaches for deriving the transform, focusing on both the process and the result.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant asks for the Laplace Transform of f(x) = e^{bx} sin(ax).
  • Another participant provides a link to Wolfram Alpha as a resource for the Laplace Transform.
  • A subsequent reply indicates that the participant has already used the resource but seeks to understand the underlying process.
  • One suggestion involves writing the integral as ∫ e^{(b-s)x} sin(ax) dx and integrating by parts twice.
  • Another participant proposes an alternative method using the identity sin(ax) = (e^{iax} - e^{-iax})/(2i), suggesting it may simplify the process.

Areas of Agreement / Disagreement

Participants present different methods for calculating the Laplace Transform, but there is no consensus on which method is preferred or more effective.

Contextual Notes

Some methods may depend on familiarity with integration techniques or complex exponentials, and the discussion does not resolve which approach is superior.

Who May Find This Useful

Readers interested in Laplace Transforms, mathematical techniques for integration, or those seeking to understand different methods for solving similar problems may find this discussion relevant.

roshan2004
Messages
140
Reaction score
0
What is the Laplace Transform of [tex]f(x)=e^{bx}.sin ax[/tex]?
 
Physics news on Phys.org
http://www.wolframalpha.com/input/?i=laplace+transform+of+e^{bx}+sin+ax
 
hamster143 said:
http://www.wolframalpha.com/input/?i=laplace+transform+of+e^{bx}+sin+ax
Yes,I have already tried it, but I want to know the process as well.
 
You write down the integral as [itex]\int e^{(b-s)x} sin ax dx[/itex] and integrate by parts twice.
 
Or you write sin(ax) = (eiax - e-iax)/2i, which is far easier.
 

Similar threads

Graduate Applying the Laplace transform to solve Differential equations
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Laplace transform of derivatives
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Laplace transform of a simple equation (Simple question)
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Understanding the Laplace Transform of cos(t)/t
  • · Replies 7 ·
Replies
7
Views
7K
Undergrad On Laplace transform of derivative
  • · Replies 17 ·
Replies
17
Views
4K
Undergrad Convergence of this Laplace transformation
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad On a bijective Laplace transform
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Laplace transform linearity problem
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Solving a differential equation using Laplace transform
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Laplace Transform of Sign() or sgn() functions
  • · Replies 1 ·
Replies
1
Views
4K