The system shown in the figure below consists of a cantilever beam (with flexural rigidity $EI$ and negligible mass), a spring (with spring constant $K$ and negligible mass) and a block of mass $m$. Assuming a lumped parameter model for the system, the fundamental natural frequency ($\omega_n$) of the system is

$\sqrt{\frac{3EI}{L^3} + K \over m}$

$\sqrt{\frac{EI}{L^3} + K \over m}$

$\sqrt{\frac{3EI}{L^3} + K \over 2m}$

$\sqrt{\frac{EI}{L^3} + K \over 2m}$

GATE 2025 Mechanical Engineering Q42 — Mechanical Engineering

GATE 2025Set MasterQ42MCQanswer keyexplanation soonmedium

Mechanical Engineering · Vibrations

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Figure from the original GATE 2025 paper. (IIT Roorkee archive)

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Recurring concept

Vibrations has appeared in GATE Mechanical Engineering 43 times across 20 years (2019, 2022, 2024, 2025, 2026, ...).