71. Given the transfer function
$G(s)=\frac{121}{s^2+13.2s+121}$ of a system. Which of the following characteristics does it have?
- Overdamped and settling time 1.1 s
- Underdamped and setting time 0.6 s
- Critically damped and settling time 0.8 s
- Underdamped and settling time 0.707 s
72. A linear time-invariant system, initially at rest when subjected to a unit step input gave response
c(t) = te-t (t ≥ 0). The transfer function of the system is
- $\frac{s}{(s+1)^2}$
- $\frac{1}{s(s+1)^2}$
- $\frac{1}{(s+1)^2}$
- $\frac{1}{(s+1)}$
73. The open-loop transfer function of a unity feedback system is given by $\frac{K}{s(s+1)}$. If the value of gain K is such that the system is critically damped, the closed-loop poles of the system will lie at
- -0.5 and -0.5
- ± j0.5
- 0 and -1
- 0.5 ± j0.5
74. The steady-state error due to a ramp input for a type two system is equal to
- infinite
- zero
- non-zero number
- constant
75. A second-order control system is defined by the following differential equation:
$4\frac{\mathrm{d^2}c(t) }{\mathrm{d} t^2}+8\frac{\mathrm{d} c(t)}{\mathrm{d} t}+16c(t)=16u(t)$
The damping ratio and natural frequency for this system are respectively
- 0.25 and 2 rad/s
- 0.50 and 2 rad/s
- 0.50 and 4 rad/s
- 0.25 and 4 rad/s
