Question

The inverse Laplace transform of F(s) = \(\frac{2}{s+c}e^{-bs}\) is _____________

(a) 2e^-k (t+b) u (t+b)

(b) 2e^-k (t-b) u (t-b)

(c) 2e^k (t-b) u (t-b)

(d) 2e^k (t-b) u (t+b)

I had been asked this question in semester exam.

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

Answer 1

Right option is (b) 2e^-k (t-b) u (t-b)

The explanation is: Let G(s) = \(\frac{2}{s+c}\)

Or, G (t) = L^-1{G(s)} = 2e^-ct

∴ F (t) = L^-1{G(s) e^-bs}

= 2e^-k (t-b) u (t-b).