Question

What should i write there can you help

Answer 1

F(s) = 1/(s² +9²)

Explanation:

You want the function F(s) given that F(s+2) = 1/(s² +4s +85).

Solution

You determined on the first line that ...

`F(s+2)=(1)/(s^2+4s+85)=(1)/((s+2)^2+9^2)`

To find F(s), replace (s+2) with s.

`\boxed{F(s) = (1)/(s^2+9^2)}`

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Additional comment

As you have already figured out, this compares to ...

`\mathcal{L}(sin((\omega t)))=(\omega)/(s^2+\omega^2)`

where ω = 9.