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engineering
mechanical vibration analysis
Mechanical Vibrations 6th Edition Singiresu S Rao - Solutions
True or False.Consider the sum of harmonic motions, \(x(t)=x_{1}(t)+x_{2}(t)=A \cos (\omega t+\alpha)\), with \(x_{1}(t)=15 \cos \omega t\) and \(x_{2}(t)=20 \cos (\omega t+1)\). The phase angle \(\alpha\) is given by \(1.57 \mathrm{rad}\).
Fill in the Blank.Systems undergo dangerously large oscillations at ________.
Fill in the Blank.Undamped vibration is characterized by no loss of ________.
Fill in the Blank.A vibratory system consists of a spring, damper, and ________.
Fill in the Blank.If a motion repeats after equal intervals of time, it is called a(n) _______.
Fill in the Blank.When acceleration is proportional to the displacement and directed toward the mean position, the motion is called ________ harmonic.
Fill in the Blank.The time taken to complete one cycle of motion is called the ________ of vibration.
Fill in the Blank.The number of cycles per unit time is called the ________ of vibration.
Fill in the Blank.Two harmonic motions having the same frequency are said to be ________.
Fill in the Blank.The angular difference between the occurrence of similar points of two harmonic motions is called ________.
Fill in the Blank.Continuous or distributed systems can be considered to have ________ number of degrees of freedom.
Fill in the Blank.Systems with a finite number of degrees of freedom are called ________ systems.
Fill in the Blank.The number of degrees of freedom of a system denotes the minimum number of independent ________ necessary to describe the positions of all parts of the system at any instant of time.
Fill in the Blank.If a system vibrates due to initial disturbance only, it is called ________ vibration.
Fill in the Blank.If a system vibrates due to an external excitation, it is called ________ vibration.
Fill in the Blank.Resonance denotes the coincidence of the frequency of external excitation with a(n) frequency of the system.
Fill in the Blank.\(\overline{\text { A function }} f(t)\) is called an odd function if ________.
Fill in the Blank.The ________ range expansions can be used to represent functions defined only in the interval 0 to \(\tau\).
Fill in the Blank.________ analysis deals with the Fourier series representation of periodic functions.
Fill in the Blank.The rotational speed of \(1000 \mathrm{rpm}\) (revolutions per minute) is equivalent to ________ radians/s.
Fill in the Blank.When the speed of a turbine is \(6000 \mathrm{rpm}\), it takes ________ seconds for the turbine to complete one revolution.
The world's first seismograph was invented in(a) Japan(b) China(c) Egypt
The first experiments on simple pendulums were conducted by(a) Galileo(b) Pythagoras(c) Aristotle
The Philosophiae Naturalis Principia Mathematica was published by(a) Galileo(b) Pythagoras(c) Newton
Mode shapes of plates, by placing sand on vibrating plates, were first observed by(a) Chladni(b) D'Alembert(c) Galileo
The thick beam theory was first presented by(a) Mindlin(b) Einstein(c) Timoshenko
The number of degrees of freedom of a simple pendulum is:(a) 0(b) 1(c) 2
Vibration can be classified in(a) one way(b) two ways(c) several ways
Gibbs' phenomenon denotes an anomalous behavior in the Fourier series representation of a(a) harmonic function(b) periodic function(c) random function
The graphical representation of the amplitudes and phase angles of the various frequency components of a periodic function is known as a(a) spectral diagram(b) frequency diagram(c) harmonic diagram
When a system vibrates in a fluid medium, the damping is(a) viscous(b) Coulomb(c) solid
When parts of a vibrating system slide on a dry surface, the damping is(a) viscous(b) Coulomb(c) solid
When the stress-strain curve of the material of a vibrating system exhibits a hysteresis loop, the damping is(a) viscous(b) Coulomb(c) solid
The equivalent spring constant of two parallel springs with stiffnesses \(k_{1}\) and \(k_{2}\) is(a) \(k_{1}+k_{2}\)(b) \(\frac{1}{\frac{1}{k_{1}}+\frac{1}{k_{2}}}\)(c) \(\frac{1}{k_{1}}+\frac{1}{k_{2}}\)
The equivalent spring constant of two series springs with stiffnesses \(k_{1}\) and \(k_{2}\) is(a) \(k_{1}+k_{2}\)(b) \(\frac{1}{\frac{1}{k_{1}}+\frac{1}{k_{2}}}\)(c) \(\frac{1}{k_{1}}+\frac{1}{k_{2}}\)
The spring constant of a cantilever beam with an end mass \(m\) is(a) \(\frac{3 E I}{l^{3}}\)(b) \(\frac{l^{3}}{3 E I}\)(c) \(\frac{W l^{3}}{3 E I}\)
If \(f(-t)=f(t)\), function \(f(t)\) is said to be(a) even(b) odd(c) continuous
Pythagoras (582-507 B.C.)a. published a book on the theory of soundb. first person to investigate musical sounds on a scientific basisc. wrote a treatise called Introduction to Harmonicsd. founder of modern experimental sciencee. invented the world's first seismograph
Euclid (300 B.C.)a. published a book on the theory of soundb. first person to investigate musical sounds on a scientific basisc. wrote a treatise called Introduction to Harmonicsd. founder of modern experimental sciencee. invented the world's first seismograph
Zhang Heng (132 A.D.)a. published a book on the theory of soundb. first person to investigate musical sounds on a scientific basisc. wrote a treatise called Introduction to Harmonicsd. founder of modern experimental sciencee. invented the world's first seismograph
Galileo (1564-1642)a. published a book on the theory of soundb. first person to investigate musical sounds on a scientific basisc. wrote a treatise called Introduction to Harmonicsd. founder of modern experimental sciencee. invented the world's first seismograph
Rayleigh (1877)a. published a book on the theory of soundb. first person to investigate musical sounds on a scientific basisc. wrote a treatise called Introduction to Harmonicsd. founder of modern experimental sciencee. invented the world's first seismograph
Imbalance in diesel enginesa. can cause failure of turbines and aircraft enginesb. cause discomfort in human activity during metal cuttingc. can cause wheels of locomotives to rise off the trackd. can cause failure of bridgese. can give rise to chatter
Vibration in machine toolsa. can cause failure of turbines and aircraft enginesb. cause discomfort in human activity during metal cuttingc. can cause wheels of locomotives to rise off the trackd. can cause failure of bridgese. can give rise to chatter
Blade and disk vibrationa. can cause failure of turbines and aircraft enginesb. cause discomfort in human activity during metal cuttingc. can cause wheels of locomotives to rise off the trackd. can cause failure of bridgese. can give rise to chatter
Wind-induced vibrationa. can cause failure of turbines and aircraft enginesb. cause discomfort in human activity during metal cuttingc. can cause wheels of locomotives to rise off the trackd. can cause failure of bridgese. can give rise to chatter
Transmission of vibrationa. can cause failure of turbines and aircraft enginesb. cause discomfort in human activity during metal cuttingc. can cause wheels of locomotives to rise off the trackd. can cause failure of bridgese. can give rise to chatter
\(k_{1}, k_{2}, k_{3}\), and \(k_{4}\) are in parallela. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000 \mathrm{~N} / \mathrm{m}\)g.
\(k_{1}, k_{2}, k_{3}\), and \(k_{4}\) are in seriesa. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000 \mathrm{~N} / \mathrm{m}\)g. \(29,500
\(k_{1}\) and \(k_{2}\) are in parallel \(\left(k_{\mathrm{eq}}=k_{12}\right)\)a. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000 \mathrm{~N}
\(k_{3}\) and \(k_{4}\) are in parallel \(\left(k_{\text {eq }}=k_{34}\right)\)a. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000 \mathrm{~N}
\(k_{1}, k_{2}\), and \(k_{3}\) are in parallel \(\left(k_{\text {eq }}=k_{123}\right)\)a. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000
\(k_{123}\) is in series with \(k_{4}\)a. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000 \mathrm{~N} / \mathrm{m}\)g. \(29,500 \mathrm{~N} /
\(k_{2}, k_{3}\), and \(k_{4}\) are in parallel \(\left(k_{\text {eq }}=k_{234}\right)\)a. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000
\(k_{1}\) and \(k_{234}\) are in seriesa. \(16,007.75 \mathrm{~N} / \mathrm{m}\)b. \(52,500 \mathrm{~N} / \mathrm{m}\)c. \(64,500 \mathrm{~N} / \mathrm{m}\)d. \(3310.078 \mathrm{~N} / \mathrm{m}\)e. \(2044.674 \mathrm{~N} / \mathrm{m}\)f. \(61,000 \mathrm{~N} / \mathrm{m}\)g. \(29,500 \mathrm{~N} /
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