GATE 2021 CE (CE2) – Question 48
A fixed-fixed beam is represented by a 10 kg lumped mass at its midpoint. Its flexural stiffness is $4\pi^2$ kN/m. Find natural frequency in Hz (integer).
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Correct answer: 10 to 10
Explanation
Convert stiffness to $4000\pi^2$ N/m. Angular frequency is $\omega_n=\sqrt{k/m}=\sqrt{400\pi^2}=20\pi$ rad/s. Divide by 2π to obtain **10 Hz**. The supplied stiffness already represents the beam, so no additional beam stiffness factor is required.