1

### GATE ECE 2009

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown. The gain and phase margins of G(s) for closed loop stability are
A
6 dB and $180^\circ$
B
3 dB and $180^\circ$
C
6 dB and $90^\circ$
D
3 dB and $90^\circ$
2

### 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
${{1125} \over {s2 + 25s + 225}}$
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 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
${{j\omega } \over {2 + j\omega }}$
4

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

### EXAM MAP

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