Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Find the initial and final values of the foll... Start Learning for Free
Find the initial and final values of the following function:
F(s) = 12(s+1)/s(s+2)^2(s+3)
- a)1,∞
- b)0,∞
- c)∞,1
- d)0,1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the initial and final values of the following function:F(s) = 12(...
Answer: d
Explanation: Using final and initial values theorem directly to find initial and final values but keeping in mind that final value theorem is applicable for stable systems only.
Explanation: Using final and initial values theorem directly to find initial and final values but keeping in mind that final value theorem is applicable for stable systems only.
Most Upvoted Answer
Find the initial and final values of the following function:F(s) = 12(...
The initial value of the function is 0, as there are no poles or residues at s=0.
To find the final value, we need to take the limit as s approaches infinity. We can use partial fraction decomposition to simplify the function:
F(s) = 12(s+1)/[s(s+2)^2(s+3)]
= A/s + B/(s+2) + C/(s+2)^2 + D/(s+3)
Multiplying both sides by the denominator and equating coefficients, we get:
A(s+2)^2(s+3) + B(s)(s+2)(s+3) + C(s)(s+3) + D(s)(s+2)^2 = 12(s+1)
Setting s=-2 and s=-3 to eliminate the terms with A, B, and C, we get:
D(-2)(-2+2)^2 = 12(-2+1)
D = -1
Substituting this value back into the equation above and simplifying, we get:
A = 0
B = 0
C = 4
D = -1
Therefore, the partial fraction decomposition of F(s) is:
F(s) = 4/(s+2)^2 - 1/(s+3)
Taking the limit as s approaches infinity, we see that the second term goes to zero, while the first term approaches 0, since it is a second-order pole. Therefore, the final value of the function is 0.
To find the final value, we need to take the limit as s approaches infinity. We can use partial fraction decomposition to simplify the function:
F(s) = 12(s+1)/[s(s+2)^2(s+3)]
= A/s + B/(s+2) + C/(s+2)^2 + D/(s+3)
Multiplying both sides by the denominator and equating coefficients, we get:
A(s+2)^2(s+3) + B(s)(s+2)(s+3) + C(s)(s+3) + D(s)(s+2)^2 = 12(s+1)
Setting s=-2 and s=-3 to eliminate the terms with A, B, and C, we get:
D(-2)(-2+2)^2 = 12(-2+1)
D = -1
Substituting this value back into the equation above and simplifying, we get:
A = 0
B = 0
C = 4
D = -1
Therefore, the partial fraction decomposition of F(s) is:
F(s) = 4/(s+2)^2 - 1/(s+3)
Taking the limit as s approaches infinity, we see that the second term goes to zero, while the first term approaches 0, since it is a second-order pole. Therefore, the final value of the function is 0.
 | Explore Courses for Electrical Engineering (EE) exam |  |
Top Courses for Electrical Engineering (EE)View all
Top Courses for Electrical Engineering (EE)
Question Description
Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer?.
Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer?.
Solutions for Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE). Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Find the initial and final values of the following function:F(s) = 12(s+1)/s(s+2)^2(s+3)a)1,∞b)0,∞c)∞,1d)0,1Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
| Explore Courses for Electrical Engineering (EE) exam | |
Top Courses for Electrical Engineering (EE)
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
