Question

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?

(a) 0

(b) 1

(c) 2

(d) 3

I got this question in unit test.

This question is from General Properties of Inverse Laplace Transform topic in chapter Laplace Transform of Engineering Mathematics

Answer 1

Right option is (c) 2

For explanation: In the given question,

\(L^{-1} \left (\frac{3s+8}{s^2+4s+25}\right )=L^{-1} \left (\frac{3(s+2)+2}{(s+2)^2+21}\right )\)

By the first shifting property

=\(e^{-2t} L^{-1} \left (\frac{3s+2}{s^2+21}\right )\)

=\(e^{-2t} L^{-1} \left (\frac{3s}{s^2+21}\right )+e^{-2t} L^{-1} \left (\frac{2}{s^2+21}\right )\)

=\(e^{-2t} (3cos⁡(\sqrt{21}t+\frac{2sin⁡(\sqrt{21}t)}{\sqrt{21}})\).