Mechanical Vibrations
Final Exam
I. THEORY
1. What is the study of mechanical vibrations? Provide at least three examples of
engineering vibrating systems. (4 points)
2. What are the fundamental components of a vibrating system? Please elaborate. (4 points)
3. One of the most important steps in the dynamic analysis procedure is defining a
mechanical model that accurately represents the physical problem. What is the definition
of number of degrees of freedom (DOF)? In general, what is the number of DOF of a
structure, and what vibration modes should the mechanical model represent? (4 points)
4. What is the natural frequency of a system? How does one determine it in a single DOF
system? (4 points)
5. Explain and compare the difference between the three different cases of motion according
to the value of damping ratio for systems with positive mass, damping, and stiffness
coefficients. (4 points)
6. How is the response of a system where one of the physical parameters m, c, or k in the
equation of motion is negative? Please explain and elaborate. (4 points)
7. What is resonance? and when does resonance occur in a single-degree-of-freedom
system?. Please give an example. (4 points)
8. Explain the concept of natural frequencies and resonance in multi-degree-of-freedom
(MDOF) systems. (4 points)
9. Explain the concept of mode shapes in MDOF systems. (4 points)
10. What are the differences between lumped-parameter systems and distributed-parameter
systems? (Please include definitions, description of the time response, and number of
DOF). (4 points)
Indicate whether each of the following statements is true or false:
1. For a single degree-of-freedom (s.d.o.f.) system, an increase in the equivalent stiffness or
a decrease in mass or mass moment of inertia decreases natural frequency. (1 point)
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