Question

The inverse Laplace transform of F(s) = \(\frac{2}{s^2+3s+2}\) is ______________

(a) -2e^-2t + 2e^-t

(b) 2e^-2t + 2e^-t

(c) -2e^-2t – 2e^-t

(d) 2e^-t + e^-2t

I have been asked this question in exam.

My enquiry is from Problems on Initial and Final Value Theorem topic in chapter Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

Right choice is (a) -2e^-2t + 2e^-t

To explain I would say: s^2 + 3s + 2 = (s+2) (s+1)

Now, F(s) = \(\frac{A}{(s+2)} + \frac{B}{(s+1)}\)

Hence, A = (s+2) F(s) |s=-2

= \(\frac{2}{s+1}\)|s=-2 = -2

And, B = (s+1) F(s) |s=-1

= \(\frac{2}{s+2}\)|s=-1 = 2

∴ F(s) = \(\frac{-2}{(s+2)} + \frac{2}{(s+1)}\)

∴ F (t) = L^-1{F(s)}

= -2e^-2t + 2e^-t for t≥0.