Finding the inverse laplace transform of (2/(s+2)^4) using Convolution theorem.

[theBEAST]

Homework Statement

Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities:

Homework Equations

Here are the given identities:

The Attempt at a Solution

Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this identity is not on our formula sheet, so I decided to try it with convolution theorem.

What did I do wrong and also is there an easier way given the table of identities? Thanks!

 

[lurflurf]

Where did you get that flawed table? Discard it.

G(s)H(s) \rightarrow \int_0^t g(t-\tau)h(\tau) \mathop{d\tau}

Clearly both functions should depend on the integration variable.

 

[theBEAST]

Where did you get that flawed table? Discard it.

G(s)H(s) \rightarrow \int_0^t g(t-\tau)h(\tau) d\tau

Clearly both functions should depend on the integration variable.

Ahh, thanks!

This is the table that we get for our midterms and final lol

Is there an easier way to solve this with another identity? The integral is pretty messy.

 

[lurflurf]

That integral is not so bad, and you wanted to avoid using

\frac{1}{(s+a)^{n+1}} \rightarrow \frac{t^n}{n!} e^{-a \mathop{t}}

you could derive it. It helps to have a longer table with fewer errors.