What-is-the-Inverse-laplace-transform-of-S-2-S-2-4S-7-Urgent-

Question Number 194887 by Mastermind last updated on 18/Jul/23

What is the Inverse laplace transform of

\frac{S + 2}{S^{2} + 4 S + 7}

Urgent!

Answered by Dwan last updated on 19/Jul/23

\frac{s + 2}{s^{2} + 4 s + 7}

= \frac{s + 2}{{(s + 2)}^{2} + 3}

L (c o s a t) = R e (\int_{0}^{\infty} e^{- s t} e^{i a t} d t) = R e (\frac{1}{s - i a})

= \frac{s}{s^{2} + a^{2}}

L^{- 1} (\frac{s + 2}{{(s + 2)}^{2} + 3}) = c o s (\sqrt{3} t)

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