GATE ME 2016 Set 3 — Question 47
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Theory of Machines & Vibrations → Forced Vibration → Magnification & Transmissibility
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Question
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of , the ratio of the amplitude of steady state response to the static deflection of the spring is __________
Correct answer
0.49 to 0.51
Solution
Given:
Excitation frequency
Natural frequency The frequency ratio is:
The ratio of the amplitude of steady state response () to the static deflection () for an undamped system is given by the magnification factor:
Substituting :
Thus, the ratio is 0.5.
Excitation frequency
Natural frequency The frequency ratio is:
The ratio of the amplitude of steady state response () to the static deflection () for an undamped system is given by the magnification factor:
Substituting :
Thus, the ratio is 0.5.
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