1
GATE ECE 2013
+2
-0.6
The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$$, when connected in feedback as shown below, the approximate value of Ka that will reduce the time constant of the closed-loop system by one hundred times as compared to that of the open-loop system is
A
1
B
5
C
10
D
100
2
GATE ECE 2009
+2
-0.6
The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer function has these properties?
A
$$\frac{-2.24}{s^2\;+\;2.59s\;+\;1.12}$$
B
$$\frac{-3.82}{s^2\;+\;1.91s\;+\;1.91}$$
C
$$\frac{-2.24}{s^2\;-\;2.59s\;+\;1.12}$$
D
$$\frac{-3.82}{s^2\;-\;1.91s\;+\;1.91}$$
3
GATE ECE 2008
+2
-0.6
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is
A
[exp(-2t) + exp(-4t)]u(t)
B
[-4exp(-2t) + 12exp(-4t) - exp(-t)]u(t)
C
[-4exp(-2t) + 12exp(-4t)]u(t)
D
[-0.5exp(-2t) + 1.5exp(-4t)]u(t)
4
GATE ECE 2008
+2
-0.6
Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions

Group I $$P=\frac{25}{s^2+25}\;\;\;\;\;Q=\frac{36}{s^2+20s+36}$$$$$R=\frac{36}{s^2+12s+36}\;\;\;\;\;S=\frac{49}{s^2+7s+49}$$$

Group II

A
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;1\;\;\;\;\;4\;\;\;\;\;2\end{array}$$
B
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;2\;\;\;\;\;4\;\;\;\;\;1\end{array}$$
C
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\2\;\;\;\;\;1\;\;\;\;\;4\;\;\;\;\;3\end{array}$$
D
$$\begin{array}{l}P\;\;\;\;Q\;\;\;\;R\;\;\;\;S\\3\;\;\;\;\;4\;\;\;\;\;1\;\;\;\;\;2\end{array}$$
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