GATE 2016 ME (ME3) – Question 47
A single-degree-of-freedom spring–mass system is excited by a harmonic force of constant amplitude at frequency $\sqrt{3k/m}$. The ratio of steady-state displacement amplitude to static spring deflection is ______.
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Show answer and explanation
Correct answer: 0.49 to 0.51
Explanation
For harmonic force on an undamped single-degree system, displacement magnification relative to static deflection is1/|1−r²|. At r=√3 it is1/|1−3|=**0.5**. The negative signed response indicates a phase reversal, while magnification is a positive amplitude ratio.