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For a particular unity feedback system G(S)=$\frac{242(S+5)}{S(S+1)(S^2+5S+121)}$
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Arranging the above equation in time constant form,

G(S)H(S)=$\frac{242 x 5 (1+S/5)}{S(1+S)(1+\frac{5}{121} S+S^{2}\frac{1}{121} 121}$

=$\frac{10(1+S/5)}{S(1+S)(1+0.041S+S^2\frac{1}{121})}$

Comparing the denominator $(S^2+5S+121)$ with the denominator of standard equation

$S^2+2ξw_nS+w_n^2,$

$w_n^2$=121

$w_n$=11 rad/sec

$2ξw_n$=5

ξ=$\frac{5}{(2 x 11)}$

ξ=0.2

The factors are:

Constant k=10

1 pole at the origin, $\frac{1}{S}$,

Simple pole, $\frac{1}{(1+S)}$ $w_c1$=1 rad/sec

Simple pole, $\frac{1}{(1+(S/5)}$ $w_c2$=5 rad/sec

Quadratic pole, $\frac{1}{(1+0.041S+S^2/121)}$ $w_c3$=11 rad/sec

Magnetic plot.

K=10, 2logk=20dB

Correction factor, -20log2ξ=-20log(2 x 0.2)

=+7.95dB

For phase angle plot,

G(jw)H(jw)=$\frac{10(1+j\frac{w}{5})}{jw(1+jw)(1+0.041jw+\frac{(j^2 w^2)}{121})}$

=$\frac{10(1+j(\frac{w}{5})}{(jw(1+jw)(1+0.041jw-(\frac{w^2}{121}))} j^2$=-1

< G(jw)H(jw)=$\frac{\lt10+j0\lt(1+j(\frac{w}{5}))}{(\lt jw\lt1+jw\lt(1+0.041jw-(\frac{w^2}{121}))}$

<10+j0=0,

<1+j$\frac{w}{5}$=+tan$^(-1)$

$\frac{w}{5}$

< $\frac{1}{jw}$=-90

<$\frac{1}{(1+jw)}$=-$tan^(-1)w$

<1/(1+0.041jw-(w^2/121))=$\frac{-tan^(-1)(0.041w}{(1-(w^2/121))}$

Phase angle table:

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