List of top Structures Questions on Vibrations asked in GATE AE

A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness $ k = 100 \, {N/m} $, as shown in the figure. The natural frequency of free vibration of the system is ___________ rad/s (answer in integer).

A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness $ k = 100 \, {N/m} $, as shown in the figure. The natural frequency of free vibration of the system is _____________ rad/s (answer in integer).

A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness $ k = 100 \, {N/m} $, as shown in the figure. The natural frequency of free vibration of the system is \_\_\_\_\_\_ rad/s (answer in integer).
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Four free-vibration responses $P,Q,R,S$ of a single-DOF spring-mass-damper with the same initial conditions are shown. Identify which curve corresponds to: (1) Overdamped, (2) Underdamped, (3) Critically damped, (4) Undamped.

For a single degree of freedom spring-mass-damper system subjected to harmonic forcing, the part of the motion (response) that decays due to damping is known as:

The equations of motion for a two degrees of freedom undamped spring-mass system are: \[ m \ddot{x}_1 + 2k x_1 - k x_2 = 0 \] \[ m \ddot{x}_2 - k x_1 + 2k x_2 = 0 \] where $m$ and $k$ represent mass and stiffness, respectively, in SI units. The larger of the two natural frequencies is given by: \[ \omega = \alpha \sqrt{\frac{k}{m}} \, \, \text{rad/s} \] The value of $\alpha$ is .............. (rounded off to 2 decimal places).

A single degree-of-freedom spring–mass–damper system has viscous damping ratio $\zeta = 0.1$. The mass has initial displacement of $10$ cm without velocity. After exactly two complete cycles of damped oscillation, find amplitude of displacement (in cm, round off to two decimals).

For studying wing vibrations, a wing of mass $M$ and finite dimensions has been idealized by assuming it to be supported using a linear spring of equivalent stiffness $k$ and a torsional spring of equivalent stiffness $k_\theta$ as shown in the figure. The centre of gravity (CG) of the wing (idealized as an airfoil) is marked. The number of degree(s) of freedom for this idealized wing vibration model is \underline{\hspace{1cm}}. \;(Answer in integer) \begin{center} \includegraphics[width=0.5\textwidth]{08.jpeg} \end{center}

Which of the following statement(s) is/are true about harmonically excited forced vibration of a single degree–of–freedom linear spring–mass–damper system?