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The damping ratio of a system having the characteristic equation s2 + 2s + 8 = 0 is
- a)0.300 (underdamped)
- b)0.353 (underdamped)
- c)1.24 (overdamped)
- d)1.02 (overdamped)
Correct answer is option 'B'. Can you explain this answer?
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The damping ratio of a system having the characteristic equation s2 + ...
Characteristics of the System:
- The given characteristic equation is s^2 + 2s + 8 = 0.
- The damping ratio of a system is given by the formula ζ = ζ = ζ / √(ω_n^2 + ζ^2), where ω_n is the natural frequency.
Calculation:
- Comparing the given characteristic equation with the standard form s^2 + 2ζω_n s + ω_n^2 = 0, we can see that ω_n^2 = 8 and 2ζω_n = 2.
- Solving for ζ, we get ζ = 1/√2 ≈ 0.353.
Therefore, the damping ratio of the system is approximately 0.353, which falls under the category of an underdamped system. Hence, the correct answer is option 'B'.
- The given characteristic equation is s^2 + 2s + 8 = 0.
- The damping ratio of a system is given by the formula ζ = ζ = ζ / √(ω_n^2 + ζ^2), where ω_n is the natural frequency.
Calculation:
- Comparing the given characteristic equation with the standard form s^2 + 2ζω_n s + ω_n^2 = 0, we can see that ω_n^2 = 8 and 2ζω_n = 2.
- Solving for ζ, we get ζ = 1/√2 ≈ 0.353.
Therefore, the damping ratio of the system is approximately 0.353, which falls under the category of an underdamped system. Hence, the correct answer is option 'B'.
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Community Answer
The damping ratio of a system having the characteristic equation s2 + ...
Given, s2 + 2s + 8 = 0
Here, ωn = √8 rad/s = 2√2 rad/sec
system is underdamped.
Here, ωn = √8 rad/s = 2√2 rad/sec
system is underdamped.
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The damping ratio of a system having the characteristic equation s2 + 2s + 8 = 0 isa)0.300 (underdamped)b)0.353 (underdamped)c)1.24 (overdamped)d)1.02 (overdamped)Correct answer is option 'B'. Can you explain this answer?
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