\[
\omega_r = \omega_n \sqrt{1 - 2\xi^2} = 1.414
\]
\[
M_r = \frac{1}{2\xi\sqrt{1-\xi^2}} = 1.155
\]
2.
起始于B点，2s后到达C点，经过BC段
三、
1.
(1)
系统的闭环传递函数
\[
\Phi(s) = \frac{2}{s^2 + 1.6s + 1} \Rightarrow 2\xi\omega_n = 1.6, \omega_n^2 = 1 \Rightarrow \omega_n = 1, \xi = 0.8
\]
(2)
(3)
\(\xi = 0.8 > 0.707\) 不存在
2.
系统的开环传递函数
\[
G(s) = \frac{\dfrac{5}{2s+1}}{s\left(1 + \dfrac{5}{2s+1}\right)} = \frac{5}{s(2s+6)} \Rightarrow K_v = \lim_{s \to 0} sG(s) = \frac{5}{6} \Rightarrow e_{ssr} = 1.2
\]
又
\[
\frac{E(s)}{N(s)} = \frac{0 - C(s)}{N(s)} = -\frac{2s+6}{s(2s+6)+5} \Rightarrow e_{ssn} = \lim_{s \to 0} sE(s) = -1.2
\]
71