Inverse Laplace transformation

[Koshi]

Homework Statement

I'm supposed to find the inverse Laplace transformation of the following equation

Homework Equations

G(s) = s+1/s²+25

The Attempt at a Solution

I was thinking of using one of the shifting theorems because I know that L^-1 {1/s²+25} is just sin(5t) but I don't know how to get rid of the numerator.

 

[Mark44]

Homework Statement

I'm supposed to find the inverse Laplace transformation of the following equation

Homework Equations

G(s) = s+1/s²+25

The Attempt at a Solution

I was thinking of using one of the shifting theorems because I know that L^-1 {1/s²+25} is just sin(5t) but I don't know how to get rid of the numerator.

You should get into the habit of using parentheses to write rational expressions correctly.

This is how what you wrote would be interpreted:
$$G(s) = s + \frac{1}{s^2} + 25$$

Here is what I believe you really meant:
$$G(s) = \frac{s + 1}{s^2 + 25}$$

To convey what I think you meant when you write in on one line, use parentheses.
G(s) = (s + 1)/(s² + 25)

Split your expression to get G(s) = s/(s² + 25) + 1/(s² + 25). From that you can get L^-1(G(s)) = L^-1( s/(s² + 25)) + L^-1(1/(s² + 25)), both of which are straightforward.

 

[Koshi]

Here is what I believe you really meant:
$$G(s) = \frac{s + 1}{s^2 + 25}$$

Yes that is what I meant to type, my mistake.

I didn't even think of separating the numerator of the equation. But I see exactly what you mean.

Thank you so much for the help and the quick reply!