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Given a unity feedback system with G (s) =K/ s (s+4). What is the value of K for a damping ratio of 0.5?
- a)1
- b)16
- c)4
- d)2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Given a unity feedback system with G (s) =K/ s (s+4). What is the valu...
Answer: b
Explanation: Comparing the equation with the standard characteristic equation gives the value of damping factor, natural frequency and value of gain K.
Explanation: Comparing the equation with the standard characteristic equation gives the value of damping factor, natural frequency and value of gain K.
Most Upvoted Answer
Given a unity feedback system with G (s) =K/ s (s+4). What is the valu...
Given: G(s) = K/ s(s+4)
Damping ratio, ζ = 0.5
We know that the damping ratio can be calculated as follows:
ζ = damping factor/undamped natural frequency
The undamped natural frequency, ωn can be calculated as:
ωn = √(k/m)
where m is the mass of the system.
In this case, we have a unity feedback system, which means that the transfer function of the system can be written as:
G(s) = K/ s(s+4)
The characteristic equation of the system can be written as:
s^2 + 4s + K = 0
Comparing this with the standard form of the characteristic equation:
s^2 + 2ζωns + ωn^2 = 0
We can see that:
2ζωn = 4
ωn^2 = K
Substituting ζ = 0.5, we get:
2 x 0.5 x ωn = 4
ωn = 4
ωn^2 = K
K = ωn^2 = 4^2 = 16
Therefore, the value of K for a damping ratio of 0.5 is 16.
Answer: (B)
Damping ratio, ζ = 0.5
We know that the damping ratio can be calculated as follows:
ζ = damping factor/undamped natural frequency
The undamped natural frequency, ωn can be calculated as:
ωn = √(k/m)
where m is the mass of the system.
In this case, we have a unity feedback system, which means that the transfer function of the system can be written as:
G(s) = K/ s(s+4)
The characteristic equation of the system can be written as:
s^2 + 4s + K = 0
Comparing this with the standard form of the characteristic equation:
s^2 + 2ζωns + ωn^2 = 0
We can see that:
2ζωn = 4
ωn^2 = K
Substituting ζ = 0.5, we get:
2 x 0.5 x ωn = 4
ωn = 4
ωn^2 = K
K = ωn^2 = 4^2 = 16
Therefore, the value of K for a damping ratio of 0.5 is 16.
Answer: (B)
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