1
GATE ECE 2008
+2
-0.6
The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {\sqrt 3 }}$$ at 5 $$\sqrt 2$$ rad/sec. The transfer function of the system is
A
$${{500} \over {{s^2} + 10s + 100}}$$
B
$${{375} \over {s2 + 5s + 75}}$$
C
$${{720} \over {s2 + 12s + 144}}$$
D
$${{1125} \over {s2 + 25s + 225}}$$
2
GATE ECE 2008
+2
-0.6
The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function.

The output of this system to the sinusoidal input x(t) = 2cos(t) for all time 't' is

A
$$0$$
B
$${2^{ - 0.25}}\cos \left( {2t - 0.125\pi } \right)$$
C
$${2^{ - 0.5}}\cos \left( {2t - 0.125\pi } \right)$$
D
$${2^{ - 0.5}}\cos \left( {2t - 0.25\pi } \right)$$
3
GATE ECE 2007
+2
-0.6
The asymptotic Bode plot of a transfer function is shown in the figure. the transfer function G(s) corresponding to this bode plot is
A
$${1 \over {\left( {s + 1} \right)\left( {s + 20} \right)}}$$
B
$${1 \over {s\left( {s + 1} \right)\left( {s + 20} \right)}}$$
C
$${{100} \over {s\left( {s + 1} \right)\left( {s + 20} \right)}}$$
D
$${{100} \over {s\left( {s + 1} \right)\left( {1 + 0.05s} \right)}}$$
4
GATE ECE 2006
+2
-0.6
Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$ The 3-dB bandwidths of their frequency responses are, respectively
A
$$\sqrt {{a^2} - 4b,}$$ $$\sqrt {{a^2} + 4b,}$$
B
$$\sqrt {{a^2} - 4b,}$$ $$\sqrt {{a^2} - 4b,}$$
C
$$\sqrt {{a^2} + 4b,}$$ $$\sqrt {{a^2} - 4b,}$$
D
$$\sqrt {{a^2} + 4b,}$$ $$\sqrt {{a^2} + 4b,}$$
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