GATE ME 2019 Set 1 — Question 16
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Theory of Machines & Vibrations → Free Vibration → SDOF Free Vibration
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Question
The natural frequencies corresponding to the spring-mass systems I and II are and , respectively. The ratio is
Correct answer
(B) (1)/(2)
Solution
For SYSTEM I, the two springs are connected in series. The equivalent stiffness is calculated as:The natural frequency is:For SYSTEM II, the two springs are connected in parallel. The equivalent stiffness is:The natural frequency is:The ratio of the natural frequencies is:Therefore, the correct option is (B).
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