The inverse Laplace transform of functions involving $s^2+as+b$ can be found by completing the square in the denominator and using the first shifting theorem ($L\{e^{-at}f(t)\} = F(s+a)$) in conjunction with standard transform pairs for $ \cos(\omega t)$ and $\sin(\omega t)$.
The inverse Laplace transform of $\frac{1} {s^2+4s+13}$ is -
Asked in Asst. Statistical Officer (Agri. Deptt.) 2024 · Topic: Mechanics (Lagrangian Formulation (Generalized Coordinates, Euler-Lagrange Equations))
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