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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,
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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
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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 isa)2b)2√3c)4d)2√2Correct answer is option 'D'. Can you explain this answer?
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