GATE ME 2024 ME Q55: Vibrations

A vibratory system consists of mass

, a vertical spring of stiffness

and a horizontal spring of stiffness

. The end A of the horizontal spring is given a horizontal motion

. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume

kg,

kN/m, and neglect friction. The magnitude of critical driving frequency for which the oscillations of mass

tend to become excessively large is ________ rad/s (answer in integer).

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