GATE ME 2025 Set 1 — Question 42
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Strength of Materials → Beams & Columns → Deflection of Beams
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Question
The system shown in the figure below consists of a cantilever beam (with flexural rigidity and negligible mass), a spring (with spring constant and negligible mass) and a block of mass . Assuming a lumped parameter model for the system, the fundamental natural frequency () of the system is
Correct answer
(A) (3EI)/(L³) + Km
Solution
The cantilever beam and the spring are in parallel because they both undergo the same displacement at the point where the mass is attached.Stiffness of the cantilever beam at the free end is:Stiffness of the spring is .Equivalent stiffness of the system in parallel is:The fundamental natural frequency is:
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