Question

Find the inverse laplace transform of alpha/((s^2+2s+2)(s^2+(alpha)^2)?

Answer 1

\[\frac{\alpha}{s^2+\alpha^2}~*~\frac{1}{(s^2+2s+1)+1}\\\frac{\alpha}{s^2+\alpha^2}~*~\frac{1}{(s+1)^2+1}\]
\[L^{-1}\left[\frac{\alpha}{s^2+\alpha^2}\right]=sin \alpha t\]
\[L^{-1}\left[\frac{1}{(s+1)^2 +1}\right]=e^{-t}sin~t\]
now, combine. take G(s) as the first one, and F(s) as the second one. You have the form of F(s)*G(s)
formula #16 tells you that
\[\int_o^t f(t-\tau)g(\tau)d\tau\]

Answer 2

Sorry, I don't understand what you wrote. The processing math is 0%.