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

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The 3-dB bandwidth of a typical second-order system with the transfer function
C(s) = ω²_n
R(s) s² + 2ξ ω_ns + ω²_n

is given by—

1. ω_n√1-2ξ²
2. ω_n√ω² + √ξ⁴ – ξ² + 1
3. ω_n√(1 – 2ξ²) + √4ξ⁴ - 4ξ³ + 2
4. ω_n√(1 – 2ξ²) - √4ξ⁴ - 4ξ³ + 2

Correct Option: C

Refer synopsis.