GATE ECE 1994 | Frequency Response Analysis Question 67 | Control Systems

GATE ECE 1994

MCQ (Single Correct Answer)

-0.3

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

$${\omega _n}\sqrt {1 - 2{\xi ^2}} $$

$${\omega _n}\sqrt {(1 - {\xi ^2}) + \sqrt {{\xi ^4} - {\xi ^2} + 1} }$$

$${\omega _n}\sqrt {(1 - 2{\xi ^2}) + \sqrt {4{\xi ^4} - 4{\xi ^2} + 2} } $$

$${\omega _n}\sqrt {(1 - 2{\xi ^2}) - \sqrt {4{\xi ^4} - 4{\xi ^2} + 2} } $$

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