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The characteristic equation of a closed loop control system is given by s2 + 4s + 16 = 0. The resonant frequency (in radian/sec) of the system is
- a)2
- b)2√3
- c)4
- d)2√2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The characteristic equation of a closed loop control system is given b...
Given, s2 + 4s+ 16 = 0
or
∴ ωn = 4 rad/s
and
∴ Resonant frequency,
or
∴ ωn = 4 rad/s
and
∴ Resonant frequency,
Most Upvoted Answer
The characteristic equation of a closed loop control system is given b...
To find the resonant frequency of the system, we need to solve the characteristic equation:
s^2 + 4s + 16 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula. In this case, let's use the quadratic formula:
s = (-b ± √(b^2 - 4ac)) / 2a
In the given equation, a = 1, b = 4, and c = 16. Plugging these values into the quadratic formula, we get:
s = (-4 ± √(4^2 - 4(1)(16))) / 2(1)
s = (-4 ± √(16 - 64)) / 2
s = (-4 ± √(-48)) / 2
s = (-4 ± √(48)i) / 2
s = (-4 ± 4√3i) / 2
s = -2 ± 2√3i
The resonant frequency is given by the imaginary part of the roots. In this case, the imaginary part is 2√3. Therefore, the resonant frequency of the system is 2√3 radian/sec.
Answer: b) 2√3
s^2 + 4s + 16 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula. In this case, let's use the quadratic formula:
s = (-b ± √(b^2 - 4ac)) / 2a
In the given equation, a = 1, b = 4, and c = 16. Plugging these values into the quadratic formula, we get:
s = (-4 ± √(4^2 - 4(1)(16))) / 2(1)
s = (-4 ± √(16 - 64)) / 2
s = (-4 ± √(-48)) / 2
s = (-4 ± √(48)i) / 2
s = (-4 ± 4√3i) / 2
s = -2 ± 2√3i
The resonant frequency is given by the imaginary part of the roots. In this case, the imaginary part is 2√3. Therefore, the resonant frequency of the system is 2√3 radian/sec.
Answer: b) 2√3
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