Laplace Transformation Convolution Integral

  • Thread starter bmb2009
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  • #1
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Homework Statement



I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got

Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2)

the answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ

We are allowed to use laplace transformation tables but what I don't understand is how to factor the terms in the Y(s) equation into a form which correlates in the base transformations. Any help would be great. Thanks



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Answers and Replies

  • #2
LCKurtz
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Homework Statement



I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got

Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2)

the answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ

Why is there a ##t## variable in your expression for ##Y(s)##?
 
  • #3
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Why is there a ##t## variable in your expression for ##Y(s)##?

My bad it's G(s) which is not explicitly defined
 
  • #4
vela
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Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2)
Is there some reason you didn't combine the last two terms into 9/(s+2)2?

the answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ
If this is the answer, you need to recheck your earlier work for errors.
 

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