Question

Decide whether or not the Final Value Theorem is applicable to the following functions. If not, indicate why you cannot apply it. If so, apply the Final Value Theorem. Note: you do not need to perform the inverse Laplace transform.a. X(s)= s/3s+7b. X(s)= 10/3s^2+7s+4

Answer 1

Answer:

a) Yes applicable, x(∞) = 0

b) Yes applicable, x(∞) = 0

Explanation:

Final Value Theroem indicates that final value of x(t) can be found by Laplace Transform X(s) as follows:

$x(\infty)= \lim\limits_{s \to0} sX(s)$

$a) X(s)= \frac{s}{3s+7}$

Since the pole is at left side, FVT is applicable

$x(\infty)= \lim\limits_{s \to0} s\frac{s}{3s+7}=0$

$b) X(s)= \frac{10}{3s^2+7s+4}$

$\frac{10}{3s^2+7s+4}= \frac{10}{(3s+4 )(s+1)}$

Since the poles are at left side, FVT is applicable

$x(\infty)= \lim\limits_{s \to0} s \frac{10}{(3s+4 )(s+1)}=0$