5. Dynamics and Control

Vibrations — Quiz

Test your understanding of vibrations with 5 practice questions.

Practice Questions

Question 1

Consider a two-degree-of-freedom undamped system in which two identical masses $m=1\,\mathrm{kg}$ are each connected to ground by a spring of stiffness $k=100\,\mathrm{N/m}$ and also connected to each other by a spring of stiffness $k$. What are the natural frequencies $\omega_1$ and $\omega_2$ (in rad/s)?

Question 2

In a lightly damped SDOF system undergoing free vibration, the measured amplitudes of the first and third successive peaks are $x_1=10\,\mathrm{mm}$ and $x_3=5\,\mathrm{mm}$. Using logarithmic decrement over two cycles, what is the damping ratio $\zeta$?

Question 3

For a damped SDOF system with damping ratio $\zeta=0.1$, the phase angle $\phi$ between steady-state response and excitation at frequency ratio $r=2$ is $\phi=\tan^{-1}\!\bigl(\frac{2\zeta r}{1-r^2}\bigr)$. What is $\phi$ in degrees (approximate)?

Question 4

In forced vibration of a damped SDOF system, if the forcing frequency is much greater than the natural frequency ($r\gg1$), what is the approximate phase difference between the steady-state response and the applied force?

Question 5

Mode shapes of an undamped multi-degree-of-freedom system are orthogonal with respect to which matrices?