How Do You Solve This Inverse Laplace Transform Equation?

[casper12]

Homework Statement

Determine the inverse Laplace transform

Homework Equations

3s+9.
(s+3)^2+7

The Attempt at a Solution

[/B]
Hi iam new to the forum and still unsure how to make the equations the correct format so hope you can understand what I have typed.

I have Tried to Convert the original equation into the equation below to try and use the partial fractions method but getting nowhere.

3s+9.
s^2+6s+16 I'm Not sure if Iam making the question more difficult, can't seem to put the division side of the equestion into brackets.

Attempt was (s-2)(s+8) but that results in s^2+6s-16 resulting in an incorrect sign. Can't seem to change the signs to make it correct.

Not sure if partial fractions method is the best method or if I'm making it more difficult than it is.

Any advice much appreciated.

 

[Mark44]

Homework Statement

Determine the inverse Laplace transform

Homework Equations

3s+9.
(s+3)^2+7

The Attempt at a Solution

[/B]
Hi iam new to the forum and still unsure how to make the equations the correct format so hope you can understand what I have typed.

I have Tried to Convert the original equation into the equation below to try and use the partial fractions method but getting nowhere.

3s+9.
s^2+6s+16I'm Not sure if Iam making the question more difficult, can't seem to put the division side of the equestion into brackets.

Attempt was (s-2)(s+8) but that results in s^2+6s-16 resulting in an incorrect sign. Can't seem to change the signs to make it correct.

Not sure if partial fractions method is the best method or if I'm making it more difficult than it is.

Any advice much appreciated.

Write your expression as $\frac{3(s + 3)}{(s + 3)^2 + 7}$
The s + 3 expressions represent a translation to the left of $\frac{3s}{s^2 + 7}$. If you can recognize what the inverse Laplace Transform of this expression is, and take care of the translation represented by s + 3, you should be able to answer your question.

Regarding using partial fractions, your factorization of (s - 2)(s + 8) is obviously wrong, as this doesn't give you s² + 6s + 16. This quadratic doesn't factor into linear factors with real coefficients, so that technique is not useful here.

 

[Mark44]

Thread closed. The original thread is in the Engineering & CS Homework section.