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 __________