(a)
Let’s determine the inverse Laplace Transform of \(\displaystyle F(s)=\frac {3s^3-2s^2+7s}{(s^2-2s+1)(s^2+2s+5)}\).
(i)
First let’s fully-factor the denominator.
(ii)
Let’s find a PFD for \(F(s)\), using the Heaviside Cover-Up Method wherever possible.
(iii)
Let’s find the inverse Laplace Transform of \(F(s)\).
(b)
Let’s determine the inverse Laplace transform of \(\displaystyle F(s)=\frac {s^2+4s+12}{s^4+8s^2+16}\).