GATE 2016 ME (ME1) – Question 21
A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.
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Correct answer: 19.9 to 20.1
Explanation
Static deflection is F0/k=100/10000=0.01m. At excitation frequency equal to the undamped natural frequency(r=1), dynamic magnification is1/(2ζ)=1/(2·0.25)=2. Therefore amplitude is **20mm**. The true displacement peak for this damped system occurs at r=sqrt(1−2ζ²), and would be about20.66mm; the official answer uses r=1.