# For the Bode plot of the system $G(s)=\frac{10}{0.66s^2+2.33s+1}$ the corner frequencies are:

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For the Bode plot of the system

$G(s)=\frac{10}{0.66s^2+2.33s+1}$ the corner frequencies are:

1. 0.66 and 0.33
2. 0.22 and 2.00
3. 0.30 and 2.33
4. 0.50 and 3.00

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Correct Answer - Option 4 : 0.50 and 3.00

Concept:

Corner frequency:

The point in Bode plot, where slope changes i.e. location of poles & zeros.

Calculation:

$G\left( s \right) = \frac{{10}}{{0.66{s^2} + 2.33s + 1}}$

$= \frac{{15.15}}{{\left( {s + 0.5} \right)\left( {s + 3.03} \right)}}$

From above open loop transfer function we get,

Poles = - 0.5, - 3.03

No of corner frequencies = 2

Given system have corner frequency = 0.5, 3.03

Note:

In general, bode plot will have transfer function in time constant form.

i.e.

$G\left( s \right) = \frac{{10}}{{0.5\left( {\frac{s}{{0.5}} + 1} \right)3.03\left( {\frac{s}{{3.03}} + 1} \right)}} = \frac{{6.6}}{{\left( {\frac{s}{{0.5}} + 1} \right)\left( {\frac{s}{{3.03}} + 1} \right)}}$

where, std. the open-loop transfer function for bode plot;

$G\left( s \right) = \frac{K}{{\left( {\frac{s}{{{w_{{c_1}}}}} + 1} \right)\left( {\frac{s}{{{w_{{c_2}}} + 1}}} \right)}};$

By comparing;

K = 6.6

${w_{{c_1}}}$ & ${w_{{c_2}}}$ are corner frequencies.