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Consider a system with transfer function G(s) = s+6/Ks2+s+6. Its damping ratio will be 0.5 when the values of k is:
- a)2/6
- b)3
- c)1/6
- d)6
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider a system with transfer function G(s) = s+6/Ks2+s+6. Its dampi...
Answer: c
Explanation: s+6/K[s2+s/K+6/K] Comparing with s2+2Gw+w2
w= √6/K
2Gw=1/K
2*0.5*√6/K =1/K
K=1/6.
Explanation: s+6/K[s2+s/K+6/K] Comparing with s2+2Gw+w2
w= √6/K
2Gw=1/K
2*0.5*√6/K =1/K
K=1/6.
Most Upvoted Answer
Consider a system with transfer function G(s) = s+6/Ks2+s+6. Its dampi...
Solution:
Given transfer function is G(s) = s 6/Ks2 + s 6
Damping ratio is given by ζ = 0.5
Damping ratio is given by ζ = ζn/√(1 – ζ^2)
where ζn is the natural damping ratio
Natural frequency is given by ωn = √(K/1)
Damping ratio is given by ζ = 1/2 = ζn/√(1 – ζ^2)
Solving for ζn, we get
ζn = ζ√(1 – ζ^2)
Substituting the given values, we get
ζn = 0.5√(1 – 0.5^2) = 0.433
Natural frequency is given by
ωn = √(K/1)
ωn^2 = K
Substituting the value of natural frequency, we get
(0.433)^2 = 6/K
K = (0.433)^2 × 6 = 1/6
Hence, the value of k is 1/6.
Given transfer function is G(s) = s 6/Ks2 + s 6
Damping ratio is given by ζ = 0.5
Damping ratio is given by ζ = ζn/√(1 – ζ^2)
where ζn is the natural damping ratio
Natural frequency is given by ωn = √(K/1)
Damping ratio is given by ζ = 1/2 = ζn/√(1 – ζ^2)
Solving for ζn, we get
ζn = ζ√(1 – ζ^2)
Substituting the given values, we get
ζn = 0.5√(1 – 0.5^2) = 0.433
Natural frequency is given by
ωn = √(K/1)
ωn^2 = K
Substituting the value of natural frequency, we get
(0.433)^2 = 6/K
K = (0.433)^2 × 6 = 1/6
Hence, the value of k is 1/6.
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