Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > The unit step response of a second order syst...
Start Learning for Free
The unit step response of a second order system is = 1-e-5t-5te-5t . Consider the following statements:
1. The under damped natural frequency is 5 rad/s.
2. The damping ratio is 1.
3. The impulse response is 25te-5t.
Which of the statements given above are correct?
1. The under damped natural frequency is 5 rad/s.
2. The damping ratio is 1.
3. The impulse response is 25te-5t.
Which of the statements given above are correct?
- a)Only 1 and 2
- b)Only 2 and 3
- c)Only 1 and 3
- d)1,2 and 3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The unit step response of a second order system is = 1-e-5t-5te-5t. Co...
Answer: d
Explanation: C(s) = 1/s-1/s+5-5/(s+5)^2
C(s) = 25/s(s2+10s+25)
R(s) = 1/s
G(s) = 25/(s2+10s+25 )
w= √25
w = 5 rad/sec
G = 1.
Explanation: C(s) = 1/s-1/s+5-5/(s+5)^2
C(s) = 25/s(s2+10s+25)
R(s) = 1/s
G(s) = 25/(s2+10s+25 )
w= √25
w = 5 rad/sec
G = 1.
Most Upvoted Answer
The unit step response of a second order system is = 1-e-5t-5te-5t. Co...
Explanation:
To determine the correctness of the given statements, let's analyze each statement separately.
Statement 1: The underdamped natural frequency is 5 rad/s.
The unit step response of a second-order system is given by:
y(t) = 1 - e^(-ζωn*t) * (cos(ωd*t) + (ζ/√(1-ζ^2))*sin(ωd*t))
where ζ is the damping ratio and ωn is the undamped natural frequency.
Comparing the given unit step response with the general form, we can see that e^(-5t) term corresponds to e^(-ζωn*t) term in the general form. Therefore, we can conclude that ζωn = 5.
Since the system is underdamped, the damping ratio ζ should be less than 1. From the given information, we cannot determine the exact value of ζ. So, statement 1 is partially correct.
Statement 2: The damping ratio is 1.
From the previous analysis, we found that ζωn = 5. If we assume ζ = 1, then ωn = 5/ζ = 5. Therefore, the damping ratio is not equal to 1. So, statement 2 is incorrect.
Statement 3: The impulse response is 25te^(-5t).
The impulse response of a second-order system is given by:
h(t) = (ωn^2/√(1-ζ^2))*e^(-ζωn*t)*sin(ωd*t)
Comparing the given impulse response with the general form, we can see that the given impulse response does not match the general form. Therefore, the statement 3 is incorrect.
Conclusion:
From the analysis above, we can conclude that only statement 1 is correct. Therefore, the correct answer is option 'D' - 1, 2, and 3.
To determine the correctness of the given statements, let's analyze each statement separately.
Statement 1: The underdamped natural frequency is 5 rad/s.
The unit step response of a second-order system is given by:
y(t) = 1 - e^(-ζωn*t) * (cos(ωd*t) + (ζ/√(1-ζ^2))*sin(ωd*t))
where ζ is the damping ratio and ωn is the undamped natural frequency.
Comparing the given unit step response with the general form, we can see that e^(-5t) term corresponds to e^(-ζωn*t) term in the general form. Therefore, we can conclude that ζωn = 5.
Since the system is underdamped, the damping ratio ζ should be less than 1. From the given information, we cannot determine the exact value of ζ. So, statement 1 is partially correct.
Statement 2: The damping ratio is 1.
From the previous analysis, we found that ζωn = 5. If we assume ζ = 1, then ωn = 5/ζ = 5. Therefore, the damping ratio is not equal to 1. So, statement 2 is incorrect.
Statement 3: The impulse response is 25te^(-5t).
The impulse response of a second-order system is given by:
h(t) = (ωn^2/√(1-ζ^2))*e^(-ζωn*t)*sin(ωd*t)
Comparing the given impulse response with the general form, we can see that the given impulse response does not match the general form. Therefore, the statement 3 is incorrect.
Conclusion:
From the analysis above, we can conclude that only statement 1 is correct. Therefore, the correct answer is option 'D' - 1, 2, and 3.
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Similar Electrical Engineering (EE) Doubts
Top Courses for Electrical Engineering (EE)View all
Question Description
The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer?.
The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer?.
Solutions for The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct 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 The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The unit step response of a second order system is = 1-e-5t-5te-5t. Consider the following statements:1. The under damped natural frequency is 5 rad/s.2. The damping ratio is 1.3. The impulse response is 25te-5t.Which of the statements given above are correct?a)Only 1 and 2b)Only 2 and 3c)Only 1 and 3d)1,2 and 3Correct 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
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily