What Is the Correct Inverse Laplace Transform of \( \frac{s+1}{s^2 - 4s + 4} \)?

In summary, using the partial fractions method, the inverse Laplace transform of s+1/s^2-4s+4 is e^2t + 3te^2t. However, an online Fourier-Laplace calculator gives a different result of e^2t + 3e^2t, which is correct. It seems there was a mistake made while using the partial fractions method.
  • #1
cabellos
77
1
inverse laplace question help please...

i am trying find the inverse laplace transfor of s+1/s^2 -4s +4

using partial fractions and solving my answer is e^2t + 3e^2t

however checking this in an online fourier-laplace calculator it comes up with e^2t + 3te^2t

who is correct? could you show me how you get your answer please...

thanks
 
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  • #2
Hello cabellos,

I get the same result as your calculator. You might have made a mistake while using the partial fractions method.

[tex]\frac{s+1}{s^2-4s+4}=\frac{s+1}{(s-2)^2}=\frac{1}{s-2}+\frac{3}{(s-2)^2}[/tex]

Regards,

nazzard
 
Last edited:
  • #3
hi, oops I am not awake :zzz: ...i used s-2 as the denominator for both A and B. Thanks
:smile:
 

FAQ: What Is the Correct Inverse Laplace Transform of \( \frac{s+1}{s^2 - 4s + 4} \)?

What is the inverse Laplace transform?

The inverse Laplace transform is a mathematical operation that takes a function in the Laplace domain and converts it back to the time domain. In other words, it is the process of finding the original function from its Laplace transform.

How is the inverse Laplace transform calculated?

The inverse Laplace transform can be calculated using various methods such as the partial fraction decomposition, convolution, and residue theorem. It ultimately depends on the complexity of the function and the tools available.

What is the importance of the inverse Laplace transform in science?

The inverse Laplace transform is an essential tool in mathematics and engineering, particularly in the field of control systems and signal processing. It allows us to analyze and understand the behavior of complex systems in the time domain.

Can the inverse Laplace transform be applied to any function?

In theory, the inverse Laplace transform can be applied to any function that has a Laplace transform. However, in practice, it may not always be possible to calculate the inverse transform due to the complexity of the function or the limitations of available tools.

Are there any tips for solving inverse Laplace transform problems?

Some tips for solving inverse Laplace transform problems include breaking down the function into simpler forms, using tables of Laplace transforms, and practicing with a variety of examples to gain familiarity with different techniques.

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