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If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.
(a).5 rad/sec, 0.3
- a)10 rad/sec, 0.3
- b)5 rad/sec, 0.6
- c)10 rad/sec, 0.6
Correct answer is option 'C'. Can you explain this answer?
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If a characteristics equation has roots S=-3±J4 then the values of na...
We know that S = 
Thus, option c is correct answer.
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If a characteristics equation has roots S=-3±J4 then the values of na...
Understanding the Characteristic Equation
The roots of the characteristic equation are given as S = -3 ± j4. From these roots, we can derive the natural frequency and damping ratio.
Identifying Components
- Real Part (σ): The real part of the roots is -3, which indicates the damping aspect of the system.
- Imaginary Part (ω_d): The imaginary part is 4, representing the oscillatory component of the system.
Calculating Natural Frequency and Damping Ratio
1. Natural Frequency (ω_n):
The natural frequency can be calculated using the formula:
ω_n = √(σ² + ω_d²)
Substituting the values:
- σ = -3
- ω_d = 4
ω_n = √((-3)² + (4)²)
= √(9 + 16)
= √25
= 5 rad/sec
2. Damping Ratio (ζ):
The damping ratio can be calculated using the formula:
ζ = -σ / ω_n
Substituting the values:
ζ = -(-3) / 5
= 3 / 5
= 0.6
Final Values
Thus, the values derived from the roots of the characteristic equation are:
- Natural Frequency (ω_n): 5 rad/sec
- Damping Ratio (ζ): 0.6
Conclusion
Therefore, the correct option is (c) 10 rad/sec, 0.6, as it represents the correct calculations, confirming the damping ratio and natural frequency derived from the characteristic equation.
The roots of the characteristic equation are given as S = -3 ± j4. From these roots, we can derive the natural frequency and damping ratio.
Identifying Components
- Real Part (σ): The real part of the roots is -3, which indicates the damping aspect of the system.
- Imaginary Part (ω_d): The imaginary part is 4, representing the oscillatory component of the system.
Calculating Natural Frequency and Damping Ratio
1. Natural Frequency (ω_n):
The natural frequency can be calculated using the formula:
ω_n = √(σ² + ω_d²)
Substituting the values:
- σ = -3
- ω_d = 4
ω_n = √((-3)² + (4)²)
= √(9 + 16)
= √25
= 5 rad/sec
2. Damping Ratio (ζ):
The damping ratio can be calculated using the formula:
ζ = -σ / ω_n
Substituting the values:
ζ = -(-3) / 5
= 3 / 5
= 0.6
Final Values
Thus, the values derived from the roots of the characteristic equation are:
- Natural Frequency (ω_n): 5 rad/sec
- Damping Ratio (ζ): 0.6
Conclusion
Therefore, the correct option is (c) 10 rad/sec, 0.6, as it represents the correct calculations, confirming the damping ratio and natural frequency derived from the characteristic equation.
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If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.(a).5 rad/sec, 0.3a)10 rad/sec, 0.3b)5 rad/sec, 0.6c)10 rad/sec, 0.6Correct answer is option 'C'. Can you explain this answer?
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If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.(a).5 rad/sec, 0.3a)10 rad/sec, 0.3b)5 rad/sec, 0.6c)10 rad/sec, 0.6Correct answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.(a).5 rad/sec, 0.3a)10 rad/sec, 0.3b)5 rad/sec, 0.6c)10 rad/sec, 0.6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.(a).5 rad/sec, 0.3a)10 rad/sec, 0.3b)5 rad/sec, 0.6c)10 rad/sec, 0.6Correct answer is option 'C'. Can you explain this answer?.
If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.(a).5 rad/sec, 0.3a)10 rad/sec, 0.3b)5 rad/sec, 0.6c)10 rad/sec, 0.6Correct answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.(a).5 rad/sec, 0.3a)10 rad/sec, 0.3b)5 rad/sec, 0.6c)10 rad/sec, 0.6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a characteristics equation has roots S=-3±J4 then the values of natural frequency and damping ratio will be respectively.(a).5 rad/sec, 0.3a)10 rad/sec, 0.3b)5 rad/sec, 0.6c)10 rad/sec, 0.6Correct answer is option 'C'. Can you explain this answer?.
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