Question

Find the inverse transform of:
F(s)=[2s+14]/[s^2+8s+32]=[2s+14]/[(s+4)^2+4^2]

Answer 1

= (2s + 8 + 6)/((s+4)^2 + 4^2)

= (2(s+4) + 6)/((s+4)^2 + 4^2)

= 2(s+4)/((s+4)^2 + 4^2) + 6/((s+4)^2 + 4^2)

= 2(s+4)/((s+4)^2 + 4^2) + (6/4)*4/((s+4)^2 + 4^2)

Now use the s-shifting theorem:

2cos(4t)*e^(-4t) + 3/2*sin(4t)*e^(-4t)