Page 116 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

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6. Can a nonlinear vibration problem be identified by looking at its governing differential
equation?
7. What is the difference between deterministic and random vibration? Give two practical
examples of each.
8. What methods are available for solving the governing equations of a vibration problem?
9. How do you connect several springs to increase the overall stiffness?
10. Define spring stiffness and damping constant.
11. What are the common types of damping?
12. State three different ways of expressing a periodic function in terms of its harmonics.
13. Define these terms: cycle, amplitude, phase angle, linear frequency, period, and natural
frequency.
14. How are t, v, and f related to each other?
15. How can we obtain the frequency, phase, and amplitude of a harmonic motion from the
corresponding rotating vector?
16. How do you add two harmonic motions having different frequencies?
17. What are beats?
18. Define the terms decibel and octave.
19. Explain Gibbs’ phenomenon.
20. What are half-range expansions?
1.2 Indicate whether each of the following statements is true or false:

1. If energy is lost in any way during vibration, the system can be considered to be damped.
2. The superposition principle is valid for both linear and nonlinear systems.
3. The frequency with which an initially disturbed system vibrates on its own is known as
natural frequency.
4. Any periodic function can be expanded into a Fourier series.
5. A harmonic motion is a periodic motion.
6. The equivalent mass of several masses at different locations can be found using the
equivalence of kinetic energy.
7. The generalized coordinates are not necessarily Cartesian coordinates.
8. Discrete systems are same as lumped parameter systems.
9. Consider the sum of harmonic motions, x1t2 = x 1 1t2 + x 2 1t2 = A cos1vt + a2, with
x 1 1t2 = 15 cos vt and x 2 1t2 = 20 cos1vt + 12. The amplitude A is given by 30.8088.
10. Consider the sum of harmonic motions, x1t2 = x 1 1t2 + x 2 1t2 = A cos1vt + a2, with
x 1 1t2 = 15 cos vt and x 2 1t2 = 20 cos1vt + 12. The phase angle a is given by 1.57 rad.

1.3 Fill in the blank with the proper word:
1. Systems undergo dangerously large oscillations at .
2. Undamped vibration is characterized by no loss of .
3. A vibratory system consists of a spring, damper, and .
4. If a motion repeats after equal intervals of time, it is called a(n) motion.
5. When acceleration is proportional to the displacement and directed toward the mean
position, the motion is called harmonic.
6. The time taken to complete one cycle of motion is called the of vibration.
7. The number of cycles per unit time is called the of vibration.
8. Two harmonic motions having the same frequency are said to be .
9. The angular difference between the occurrence of similar points of two harmonic motions
is called .