What is the steady state value of F (t), if it is known that F(s) = b/(s(s+1)(s+a)), where a>0?

Question

What is the steady state value of F (t), if it is known that F(s) = b/(s(s+1)(s+a)), where a>0?

(a) \(\frac{b}{a}\)

(b) \(\frac{a}{b}\)

(c) 1

(d) Cannot be determined

Answer 1

The correct choice is (a) \(\frac{b}{a}\)

The explanation: F (∞) = lims→0 s F(s)

= lims→0  \(\frac{sb}{s(s+1)(s+a)}\)

= lims→0 \(\frac{b}{(s+1)(s+a)}\)

= \(\frac{b}{a}\).