Two independent closed loop second order systems have the roots of their individual characteristic equations located at [math: −3±j4]-3\pm j4 and [math: −6±j8]-6\pm j8. The following can be said about these two systems.

Question

BlackTom AI · Accepted Answer

The question describes two independent closed-loop second-order systems with poles located at -3 ± j4 for the first and -6 ± j8 for the second.

Option analysis:
- Option B: They both will have the same damping ratio ζ.
  For a second-order system with poles at -σ ± jω_d, the damping ratio is ζ = σ / ω_n, where ω_n = sqrt(σ^2 + ω_d^2).
  - For the first pair: σ = 3 and ω_d = 4, so ω_n = sqrt(3^2 + 4^2) = 5, and ζ = σ/ω_n = 3/5 = 0.6.
  - For the second pair: σ = 6 and ω_d = 8, so ω_n = sqrt(6^2 + 8^2) = 10, and ζ = σ/ω_n = 6/10 = 0.6.
  Since both yield ζ = 0.6, the damping ratios are indeed equal.
  This equality arises because the two pole pairs are scalar multiples of each other in the complex plane (their real and imaginary parts scale by the same factor), which preserves the ratio σ/ω_n = ζ.

Notes on the other options:
- If there were alternative statements suggesting different ζ values or relationships, they would need to be evaluated against the definition ζ = σ/ω_n using the corresponding σ and ω_n for each system. In this case, the computed damping ratios coincide, so any claim asserting a difference would be incorrect.
- Without additional options provided, only the evaluation of the given statement can be performed; the conclusion about equality follows directly from the standard second-order pole form and the provided pole locations.

Two independent closed loop second order systems have the roots of their individual characteristic equations located at [math: −3±j4]-3\pm j4 and [math: −6±j8]-6\pm j8. The following can be said about these two systems.单项选择题

类似问题

Two independent closed loop second order systems have the roots of their individual characteristic equations located at −3±j4[math]-3\pm j4 and −6±j8[math]-6\pm j8. The following can be said about these two systems.

You own a bond that pays $64 in interest annually. The face value is $1,000 and the current market price is $1,021.61. The bond matures in 11 years. What is the yield to maturity?

Which of the following statements is CORRECT?

It will cost $9,600 to acquire an ice cream cart that is expected to produce cash inflows of $3,600 a year for three years. After the three years, the cart is expected to be worthless. What is the payback period?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单