Find the \(L^{-1} (\frac{s}{2s+9+s^2})\).

1.	Find the \(L^{-1} (\frac{s}{2s+9+s^2})\).
A.	\(e^{-t} \{cos⁡(2\sqrt{2t})-sin⁡(\sqrt{2t})\}\)
B.	\(e^{-t} \{cos⁡(2\sqrt{2t})-sin⁡(2\sqrt{2t})\}\)
C.	\(e^{-t} \{cos⁡(2\sqrt{2t})-cos(\sqrt{2t})\}\)
D.	\(e^{-2t} \{cos⁡(2\sqrt{2t})-sin⁡(2\sqrt{2t})\}\)
Answer» C. \(e^{-t} \{cos⁡(2\sqrt{2t})-cos(\sqrt{2t})\}\)

Discussion

The \(L^{-1} \left (\frac{3s+8}{s^2+4s+25}\right )\) is \(e^{-st} (3cos⁡(\sqrt{21}t+\frac{2sin⁡(\sqrt{21}t)}{\sqrt{21}})\). What is the value of s?
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