Laplace Transform: Get the Answers You Need

In summary, the conversation discusses techniques for calculating the inverse Laplace transform. These techniques include using a Laplace transform table and simplifying the function by factoring and expanding terms. The conversation also mentions that partial fraction decomposition may not be necessary for this specific problem. One person in the conversation also mentions solving the problem without using partial fractions.
  • #1
kukumaluboy
61
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Gimme CLue
 
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  • #2
kukumaluboy said:
Gimme CLue

You can stick that function directly into the integral formula which defines the inverse Laplace transform and try to calculate it out.

You can use a Laplace transform table. This approach starts by doing a partial fraction expansion of your function. Then the resulting sum of terms can be inverse transformed by matching with transforms in a table. Remember that a Laplace transform is a linear operator.
 
  • #3
Here's a big hint. What do you get if you differentiate the following with respect to s:

[tex]\frac s {s^2+4}[/tex]
 
Last edited:
  • #4
Investigate factoring/expanding some terms, and see what you get. In the end, I do not even think you are going to have to use a partial fraction decomposition to do the problem. The terms in the fraction are chosen with reason in this problem, i.e. it is much simpler than is written.

What have you attempted?
 
  • #5
Ok Solved! LawlQuals you were rite. I did not use partial fractions. Just simplify and the formulae can be used.
 
  • #6
LawlQuals said:
Investigate factoring/expanding some terms, and see what you get. In the end, I do not even think you are going to have to use a partial fraction decomposition to do the problem. The terms in the fraction are chosen with reason in this problem, i.e. it is much simpler than is written.

What have you attempted?

I thought he asked for a clue, not a solution. :frown:
 

Related to Laplace Transform: Get the Answers You Need

1. What is a Laplace Transform?

The Laplace Transform is a mathematical tool used to convert a function of time into a function of complex frequency. It is particularly useful in solving differential equations in engineering and physics.

2. How is a Laplace Transform calculated?

The Laplace Transform is calculated by integrating the function of time multiplied by the exponential function of -st, where s is a complex number. This results in a new function of complex frequency.

3. What are the applications of Laplace Transform?

The Laplace Transform has various applications in engineering and physics, such as solving differential equations, analyzing control systems, and studying the behavior of electrical circuits.

4. What is the difference between Laplace Transform and Fourier Transform?

The Laplace Transform is an extension of the Fourier Transform, which only converts a function of time into a function of real frequency. The Laplace Transform allows for the analysis of functions with discontinuities and exponential growth, while the Fourier Transform is limited to periodic functions.

5. How is Laplace Transform used in practical situations?

Laplace Transform is used in practical situations to solve differential equations and analyze the behavior of systems with varying inputs. It is also used in signal processing and electrical engineering to study the frequency response of systems.

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