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GATE 2019 AE – Question 35

Structures · Structural dynamics: free and forced vibration of SDOF systems and free vibration of 2-DOF systems · 1 mark · Numerical answer

In the spring–mass system shown, m=3 kg and each spring has stiffness k=20 kN/m. Find the natural frequency in Hz (nearest integer).

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Correct answer: 16 to 16

Explanation

The two left springs are in series, giving k/2. Their combination and the right spring both resist mass displacement, so $k_{eq}=k/2+k=30000$ N/m. Then $\omega_n=\sqrt{k_{eq}/m}=100$ rad/s and $f_n=\omega_n/(2\pi)=15.92$ Hz, or 16.

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