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Blizzard [7]
3 years ago
11

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
Engineering
1 answer:
LUCKY_DIMON [66]3 years ago
3 0

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

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