Inverse Laplace

Question

Answer 1

(6s² + 10s + 2)/[s(s² + 2s + 2)] = a/s + (bs + c)/(s² + 2s + 2).

So for decomposition we have: a + b = 6, 2a + c = 10, 2a = 2,; a = 1, b = 5, c = 8.

We get decomposition:

(6s² + 10s + 2)/[s(s² + 2s + 2)] = 1/s + (5s + 8)/[(s + 1)² + 1].;

L^-1{F(s)} = L^-1{1/s} + L^-1{(5s + 8)/[(s + 1)² + 1]} = 1 + L^-1{ 5(s + 1)/[(s + 1)² + 1] + 3/[(s + 1)² + 1]} =

1 + e^-t(5cost + 3sint)