Resonance Peak Frequency

Correct Answer

B — 2√2 rad/s

Concept and Reasoning

The closed-loop denominator is s²+4s+16, so ωn=4 rad/s and ζ=0.5. Since ζ<1/√2, a resonance peak exists at ωr=ωn√(1−2ζ²)=2√2 rad/s.

Calculation / Key Relation

ωr=ωn√(1−2ζ²)=4√(1−0.5)=2√2 rad/s

Exam Takeaway

Find ωn and ζ from the closed-loop denominator before using the resonance formula.

Common Mistake

Do not use ωn itself as the resonance frequency unless the damping is negligible.