GATE 2014 EC (EC2) – Question 30
A second-order system has undamped natural frequency 40 rad/s and damping ratio 0.3. Find damped natural frequency (rad/s).
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Show answer and explanation
Correct answer: 38.13 to 38.19
Explanation
For an underdamped second-order system ωd=ωn√(1−ζ²). Substituting ωn=40rad/s and ζ=0.3gives40√0.91=**38.1576rad/s**. Damping reduces the oscillation frequency below the undamped natural frequency.