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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?
Most Upvoted Answer
The unit step response of a second order system is = 1-e-5t-5te-5t. Co...
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.
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.
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The unit step response of a second order system is = 1-e-5t-5te-5t. Co...
Explanation:
The given unit step response of a second-order system is:
y(t) = 1 - e^(-5t) - 5t * e^(-5t)
To analyze the system, we need to find the natural frequency and the damping ratio.
1. The underdamped natural frequency is 5 rad/s:
To find the natural frequency, we need to find the coefficient of the exponential term in the unit step response. In this case, the coefficient is -5.
Natural frequency (ωn) = sqrt(coefficient) = sqrt(-5) = √5
So, the given statement is correct.
2. The damping ratio is 1:
To find the damping ratio, we need to find the coefficient of the linear term in the unit step response. In this case, the coefficient is -5t.
The damping ratio (ζ) is given by the formula:
ζ = coefficient / (2 * natural frequency) = (-5) / (2 * √5) = -√5 / 2
The given statement is incorrect. The damping ratio is not 1.
3. The impulse response is 25te^(-5t):
To find the impulse response, we need to differentiate the unit step response with respect to time.
Differentiating the unit step response, we get:
y'(t) = 5e^(-5t) - 5e^(-5t) - 5te^(-5t) + 25te^(-5t)
Simplifying, we get:
y'(t) = 5te^(-5t)
Comparing this with the given impulse response, we can see that they are the same.
So, the given statement is correct.
Therefore, the correct statements are:
1. The underdamped natural frequency is 5 rad/s.
3. The impulse response is 25te^(-5t).
Hence, the correct answer is option D) 1, 2, and 3.
The given unit step response of a second-order system is:
y(t) = 1 - e^(-5t) - 5t * e^(-5t)
To analyze the system, we need to find the natural frequency and the damping ratio.
1. The underdamped natural frequency is 5 rad/s:
To find the natural frequency, we need to find the coefficient of the exponential term in the unit step response. In this case, the coefficient is -5.
Natural frequency (ωn) = sqrt(coefficient) = sqrt(-5) = √5
So, the given statement is correct.
2. The damping ratio is 1:
To find the damping ratio, we need to find the coefficient of the linear term in the unit step response. In this case, the coefficient is -5t.
The damping ratio (ζ) is given by the formula:
ζ = coefficient / (2 * natural frequency) = (-5) / (2 * √5) = -√5 / 2
The given statement is incorrect. The damping ratio is not 1.
3. The impulse response is 25te^(-5t):
To find the impulse response, we need to differentiate the unit step response with respect to time.
Differentiating the unit step response, we get:
y'(t) = 5e^(-5t) - 5e^(-5t) - 5te^(-5t) + 25te^(-5t)
Simplifying, we get:
y'(t) = 5te^(-5t)
Comparing this with the given impulse response, we can see that they are the same.
So, the given statement is correct.
Therefore, the correct statements are:
1. The underdamped natural frequency is 5 rad/s.
3. The impulse response is 25te^(-5t).
Hence, the correct answer is option D) 1, 2, and 3.
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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?.
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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).
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