1

### GATE ECE 2008

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

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 frequency response H(ω) of the system in terms of angular frequency 'ω' is given by h( ω)

A
${1 \over {1 + j2\omega }}$
B
${{\sin \omega } \over \omega }$
C
${1 \over {2 + j\omega }}$
D
${{j\omega } \over {2 + j\omega }}$
3

### GATE ECE 2008

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
${2^{ - 0.5}}\cos \left( {2t - 0.25\pi } \right)$
4

### GATE ECE 2007

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
${{100} \over {s\left( {s + 1} \right)\left( {1 + 0.05s} \right)}}$

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