The 3-dB bandwidth of a typical second-order system with the transfer function $$\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{\omega _n^2}}{{{s^2} + 2\xi {\omega _n}s + {\omega ^2}}}$$

A) $${\omega _n}\sqrt {1 - 2{\xi ^2}} $$ B) $${\omega _n}\sqrt {\left( {1 - {\xi ^2}} \right) + \sqrt {{\xi ^4} - {\xi ^2} + 1} } $$ C) $${\omega _n}\sqrt {\left( {1 - 2{\xi ^2}} \right) + \sqrt {4{\xi ^4} - 4{\xi ^2} + 2} } $$ D) $${\omega _n}\sqrt {\left( {1 - 2{\xi ^2}} \right) - \sqrt {4{\xi ^4} - 4{\xi ^2} + 2} } $$

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Correct Answer: Option C

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The 3-dB bandwidth of a typical second-order system with the transfer...

The 3-dB bandwidth of a typical second-order system with the transfer function $$\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{\omega _n^2}}{{{s^2} + 2\xi {\omega _n}s + {\omega ^2}}}$$

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