Loop transfer function of a feedback system is then, the Nyquist plot of G(s) H(s) encircles - 1 + j0.
$G (s) H (s) = \frac{1}{2 s (s + \frac{1}{2})}$

once in clockwise direction

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does not encircle

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Once in anticlockwise direction

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twice in clock wise direction

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Solution

The correct option is B does not encircle
$G (s) H (s) = \frac{1}{2 s (s + \frac{1}{2})}$
Nyquist plot of the above system is,

Nyquist plot does not encircle (-1 + j0) point.

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Loop transfer function of a feedback system is then, the Nyquist plot of G(s) H(s) encircles - 1 + j0. G(s)H(s)=12s(s+12)

The correct option is B does not encircleG(s)H(s)=12s(s+12) Nyquist plot of the above system is, Nyquist plot does not encircle (-1 + j0) point.

Loop transfer function of a feedback system is then, the Nyquist plot of G(s) H(s) encircles - 1 + j0.
$G (s) H (s) = \frac{1}{2 s (s + \frac{1}{2})}$

The correct option is B does not encircle
$G (s) H (s) = \frac{1}{2 s (s + \frac{1}{2})}$
Nyquist plot of the above system is,

Nyquist plot does not encircle (-1 + j0) point.