Vibrations Test
f(-t)=-f(t)
A function f(t) is called an odd function if __________.
False
A system is said to be conservative if no energy is lost due to friction if energy-dissipating non-elastic members. If no work is done on a conservative system by an external force, then the total energy of the system remains zero
Harmonic
A system undergoing simple harmonic motion is called a __________ oscillator.
True
A system vibrating in air can be considered as a damped system
Mass
A vibratory system consists of a spring, damper, and __________
True
Coulomb damping can be called constant damping.
True
Discrete systems are same as lumped parameter systems
False
For an undamped system, the velocity leads the acceleration by pi/2
True
For an undamped system, the velocity leads the displacement by pi/2
An original disturbance
Free vibration means that the mass is set into motion, because _________ with no externally applied force other than the spring force, damper force, or gravitational force
True
Harmonic motion is a periodic motion
True
The equation of motion of a single degree of freedom system will be the same whether the mass moves in a horizontal plane or an inclined plane.
True
The equivalent mass of several masses at different locations can be found using the equivalence of kinetic energy
True
The final position of the mass is always the equilibrium position in the case of Coulomb damping.
True
The free vibration of a undamped system represents interchange of kinetic and potential energies
kinetic and potential
The free vibration of an undamped system represents interchange of __________ _________ energies.
True
The frequency with which an initially disturbed system vibrates on its own is known as natural frequency
Resonance
Systems undergo dangerously large oscillations at __________
Discrete
Systems with a finite number of degrees of freedom are called __________ systems.
0.2251
for a single degree of freedom system with m = 1, k = 2, and c = 0.5 Find Linear frequency, fn
1.4142
for a single degree of freedom system with m = 1, k = 2, and c = 0.5 Find Natural frequency, ωn
2.8284
for a single degree of freedom system with m = 1, k = 2, and c = 0.5: Find Critical damping constant, Cc
1.3919
for a single degree of freedom system with m = 1, k = 2, and c = 0.5: Find Damped frequency, ωd
0.1768
for a single degree of freedom system with m = 1, k = 2, and c = 0.5: Find Damping ratio, ς
4.4429
for a single degree of freedom system with m = 1, k = 2, and c = 0.5: Find Natural time period, τn
1.1287
for a single degree of freedom system with m = 1, k = 2, and c =0.5: Find Logarithmic decrement, δ
Loss
The __________ coefficient can be used to compare the damping capacity of different engineering materials.
Half
The __________ range expansions can be used to represent functions defined only in the interval 0 to τ.
True
The amplitude of an undamped system will not change with time
True
The amplitude of an undamped system will not change with time.
Phase difference
The angular difference between the occurrence of similar points of two harmonic motions is called __________
Percussion
The center of __________ can be used advantageously in a baseball bat.
True
The complex stiffness can be used to find the damping force in a system with hysteresis damping.
False
The damped frequency can be larger that the undamped natural frequency of the system in some cases.
True
The damped frequency can be zero in some cases.
Coordinates
The degree 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.
True
The generalized coordinates are not necessarily Cartesian coordinates
True
The hysteresis loop of the stress - strain curve of a material causes damping.
True
The logarithmic decrement can be used to find the damping ratio.
Amplitude
The logarithmic decrement denotes the rate at which the __________ of a free damped vibration decreases.
True
The loss coefficient denotes the energy dissipated per radian per unit strain energy.
Torsional
The mechanical clock represents a __________ pendulum.
True
The motion can be considered to be harmonic in the cases of hysteresis damping.
True
The motion diminishes to zero in both underdamped and overdamped cases.
Critical
The property of __________ damping is used in many practical applications such as large guns.
70.0
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k1 and k2 in parallel
18.9189
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k1 in series with k234
370.0
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k1,k2,k3 and k4 are in parallel
170
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k1,k2,k3 in parallel
11.7647
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k1,k2,k3,4k in series
91.8919
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k123 in series with k4
350.0
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k2,k3,k4 parallel
300.0
k1 = 20lb/in, k2 = 50 lb/in, k3 = 100 lb/in, k4 = 200 lb/in k3 and k4 in parallel
Simple
When acceleration is proportional to the displacement and directed towards the mean position, the motion is called __________ harmonic.
True
When a mass vibrates in a vertical direction, its weight can always be ignored in deriving the equation of motion
True
When a mass vibrates in a vertical direction, its weight can always be ignored in deriving the equation of motion.
Continues
With viscous and hysteresis damping, the motion __________ for ever, theoretically.
Harmonic
__________ analysis deals with the Fourier series representation of periodic functions.
An interval of time
Oscillatory motion may repeat itself regularly, or it may display considerable irregularity, as in the use of ground motion during an earthquake. If the motion is repeated after _________, it is called the periodic motion. The simplest type of periodic motion is harmonic motion
Natural
Rayleigh's method can be used to find the __________ frequency of a system directly.
True
Rayleigh's method is based on the principle of conservation of energy.
Natural
Resonance denotes the coincidence of the frequency of external excitation with a __________ frequency of the system.
False
The principle of conservation of energy can be used to derive the equation of motion of both damped and undamped systems.
True
Any periodic function can be expanded into Fourier series
Logarithmic
Any two successive displacements of the system, separated by a cycle, can be used to find the __________ decrement.
infinite
Continuous or distributed systems can be considered to have __________ number of degrees of freedom
Periodic
If a motion repeats after equal intervals of time, it is called a __________ motion.
True
If a rigid body oscillates about a specific reference axis, the resulting motion is called translational vibration. In this case, the displacement if the body is measured in terms of angular coordinates
Forced
If a system vibrates due to an external excitation, it is called __________ vibration
Free
If a system vibrates due to initial disturbance only, it is called __________ vibration
A soft spring
If b<0
A linear spring
If b=0
A hard spring
If b>0
False
If energy is lost in any way during vibration, the system can be considered undamped
True
In actual practice, except in a vacuum, the amplitude of free vibration diminishes gradually over time due to the resistance offered by the surrounding medium, such as air. Such vibrations are said to be damped
Heat, sound
In many practical systems, the vibrational energy is converted to _____ or _______ as a result of the reduction in the energy
Equilibrium
In the case of configuration of the spring-mass system, the mass hangs at the lower end of a spring, which is attached to a rigid support at its upper end. At rest, the mass will hang in a position called the _________, in which the upward spring force exactly balances the downward gravitational force on the mass
Frequency
The number of cycles per unit time is called the __________ of vibration
False
The superposition principle is valid for both linear and nonlinear systems
Period
The time taken to complete one cycle of motion is called the __________ of vibration.
Rigid
Torsional vibration occurs when a __________ body oscillates about an axis.
Synchronous
Two harmonic motions having the same frequency are said to be __________
Energy
Undamped vibration is characterized by no loss of __________
