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

In summary, the Laplace Transform is a mathematical tool used in Wolfram to convert a function of time into a function of complex frequency. It is used to solve differential equations and analyze systems in the frequency domain. To input a function into the Laplace Transform, use the command "LaplaceTransform[f[t], t, s]" where f[t] is the function and s is the variable in the transformed function. The Laplace Transform in Wolfram can handle piecewise functions and has various options and settings such as specifying the domain, integration method, and precision of the output. The output of the Laplace Transform is typically a rational function of the complex variable s, which represents the frequency response of the original function in the complex frequency
  • #1
roshan2004
140
0
What is the Laplace Transform of [tex]f(x)=e^{bx}.sin ax[/tex]?
 
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  • #2
http://www.wolframalpha.com/input/?i=laplace+transform+of+e^{bx}+sin+ax
 
  • #3
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.
 
  • #4
You write down the integral as [itex]\int e^{(b-s)x} sin ax dx[/itex] and integrate by parts twice.
 
  • #5
Or you write sin(ax) = (eiax - e-iax)/2i, which is far easier.
 

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

1. What is the Laplace Transform and how is it used in Wolfram?

The Laplace Transform is a mathematical tool used to convert a function of time into a function of complex frequency. In Wolfram, it is used to solve differential equations and analyze systems in the frequency domain.

2. How do I input a function into the Laplace Transform in Wolfram?

To input a function into the Laplace Transform in Wolfram, use the command "LaplaceTransform[f[t], t, s]" where f[t] is the function and s is the variable in the transformed function.

3. Can the Laplace Transform in Wolfram handle piecewise functions?

Yes, the Laplace Transform in Wolfram can handle piecewise functions. Simply input the piecewise function as you would any other function.

4. Are there any special options or settings for the Laplace Transform in Wolfram?

Yes, there are several options and settings available for the Laplace Transform in Wolfram. Some examples include specifying the domain of the transformed function, choosing the method of integration, and setting the precision of the output.

5. How do I interpret the output of the Laplace Transform in Wolfram?

The output of the Laplace Transform in Wolfram is typically given in the form of a rational function of the complex variable s. This can be interpreted as the frequency response of the original function in the complex frequency domain.

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