Question

Find the initial value of f(t) if F(s) = \(\frac{s}{(s+a)^2+ω^2}\).

(a) 0

(b) -1

(c) ∞

(d) 1

This question was posed to me during an online exam.

Question is taken from Properties of the Laplace Transform topic in portion Laplace Transform and System Design of Signals and Systems

Answer 1

Right answer is (d) 1

Best explanation: Given F(s) = \(\frac{s}{(s+a)^2+ω^2}\)

The initial value is f(0^+) = lims→∞ sF(s)

= lims→∞⁡ s \(\frac{s}{(s+a)^2+ω^2} = lim_{s→∞} \frac{1}{(1+a/s)^2+(ω/s)^2} = 1\).