Chapter 3 Oscillations and Vibrations Flashcards
equilibrium
the rest or neutral position of a system, when it is not in a back-and-forth motion.
the source of sound is the back and forth motion of a mechanical object around its equilibrium position.
oscillation
any back and forth movement between two states.
do to the force of GRAVITY
oscillator
an object that can be set into oscillation.
vibration
a back and forth motion that is mechanical, with ELASTICITY acting as the restoring force.
vibrator
an object that can be set into a back and forth motion
pendulum
a bob suspended form a fixed point on a thin arm that can swing freely back and forth when the pendulum is displaced from its rest position.
one of the most commonly used models of motion.
displacement of a pendulum
notes pg 17 & 18
will not move unless it is displaced by an external force.
inertia keeps it moving
friction will slow it down
can be plotted (shown) in a WAVE FORM GRAPH
opposite of acceleration
sinusoidal motion
the oscillation made by a pendulum is a SINE FUNCTION; therefore, the motion is often called sinusoidal motion or simple harmonic motion.
velocity of a pendulum
notes pg 19
the pendulum travels slowest at the edges of its swing, so velocity is zero at points B and D.
maximum velocity at points A,C, and E.
The post of velocity is similar to the SINE function, but shifted in time by 1/4 of the pendulum swing.
acceleration of a pendulum
notes pg 19-20
acceleration is maximum at the edges of the pendulum swing (points B and D).
acceleration is minimum through equilibrium (points A,C,E)
acceleration is a vector-involves direction.
***B is negative because the pendulum is accelerating in the negative direction.
graph for displacement and acceleration are opposites
(out of phase)
acceleration
Periodic motion
motion that repeats itself in regular intervals until it is stopped by external action.
Wave form
is a graph, NOT a wave/sound
A function representing changes of any physical quality as a function of time.
pg 21 notes
harmonic motion
a motion in which the ACCELERATION of the object is directly proportional but opposite in direction to the DISPLACEMENT (of the object from its equilibrium position).
simple harmonic motion
(sinusoidal motion)
if a single object (such as a pendulum) is moving in harmonic motion, then changes in displacement, velocity and acceleration are sinusoidal functions of time.
cycle
one full repetition of a periodic motion
frequency
pg 22-23 notes
number of cycles per second
f=number(cycles)/time(seconds)
Unit is Hertz (Hz)
1cycle/second=1Hz
inversely related to period
period
pg 22-23 notes
the time it takes to complete on cycle of a periodic motion.
Unit is a time unit (Second, millisecond)
p=time/cycles
inversely related to frequency
tuning fork
Tines are part that vibrates.
***lower frequencies that a longer time to complete one cycle
***higher frequencies complete cycle faster.
Pg 24 notes.
phase angle
Screen shots
indicates a particular stage in the cycle of MOTION using the angles from a circle as the unit of measure.
what is the wave doing at a certain time.
phase relationship
describes the difference between the phases of two periodic waveforms as they cycle through time.
phase difference
(phase offset)
the absolute difference between the phases of two waveforms with neither of them being considered as a point of reference. The maximum possible value of phase difference is 180 degrees.
phase shift
the relationship between the phase of one waveform and another where one is considered as the point of reference. (+) lead (-) lag.
in phase
when two waveforms have the same frequency and the same phase relationship.
out of phase
if two waveforms have the same frequency but the phase is not the same.
instantaneous magnitude
the magnitude of a waveform at any given moment in time.
amplitude (A)
the maximum (peak) magnitude of a periodic waveforms.
peak-to-peak magnitude
the whole range of magnitude changes within one period (1 to -1 = 2)
average magnitude (Aavr)
the average value to the magnitude calculated across the whole period of a waveform. (always 0 for periodic waveforms. complex waveforms may have an average magnitude other than 0)
unipolar average magnitude (Aua)
rectified average magnitude)
the average magnitude calculated over the whole period of the waveform with the negative half of the waveform mirror imaged (flipped up) on the positive side.
Aua = 2A/3.14 (3.7 book)
root mean square (RMS) magnitude (Arms)
glossary definition
**represents the ENERGY of the waveform
average POWER of a signal over a specific time period;
if a signal x is broken down into a set of values corresponding to n consecutive moments in time (X1, X2……,Xn) the RMS magnitude (Xrms) is equal to X1 squared, average over a specific time period, and then the square root of this average is determined.
root mean square (RMS) magnitude (Arms)
chapter definition
the Arms is defined as a constant magnitude (one value) that would produce the same power as the original quantity of the waveform (a magnitude that varies)
Arms = amplitude x .707
look at formula 3.8 pg 59 book, or 28 in notes
Example:
What is the Arms when the amplitude is 6m
Arms = 6 X .707
Arms = 4.242
Mass and spring system
a model used to study phenomena associated with simple harmonic motion including MASS, STIFFNESS, and FRICTION EFFECT
Why will the mass vibrate back and forth
Mass will vibrate back and forth in simple harmonic motion because of the interaction between ELASTICITY & INERTIA
Force on the mass
a small force applied to the mass will result in small amplitude of vibration.
a large force applied to the mass will result in a large amplitude of vibration.
Hooke’s Law of Elasticity
the force produced by an elastic object is linearly proportional to its extension.
stiffness
a mechanical property of an elastic object that describes its opposition to the change of its dimensions by an external force.
elasticity
the property of matter that allows matter to recover its form (size and shape) after it has been distorted (expanded or compressed)
A FORM OF POTENTIAL ENERTY
Resonance and Free Vibration
Closed system
a system that does not exchange its energy with the environment, so it is forever exchanging its potential energy with kinetic energy and vice versa.
only exist in theory.
Resonance and Free Vibration
Open system
a system that loses part of its energy to the surrounding environment due to the effects of friction.
Resonance and Free Vibration
Free vibration
a case in which a system is left alone to vibrate at its resonance frequency after being activated by the short application of an external force.
the back and forth vibration of a system in which no additional energy is added to the system once it is initially set into motion
Resonance and Free Vibration
resonance frequency
the frequency of the free back and forth motion (vibration. oscillation) of a system; the frequency at which a vibrating system moves back and forth when left alone.
Resonance and Free Vibration
resonance
the natural state of a vibrating system. the state in which it stays after being excited and left alone.
the state of a vibration systemic which no external force acts on the system and the system vibrates at its own frequency.
Resonance and Free Vibration
forced vibration
a vibration in which a system is forced to vibrate by a continuously or periodically applied external force.
Friction and Damped Vibration
Friction
the force that opposes the relative motion (dynamic friction) or tendency to such motion (static friction) of two bodies in contact and causes the conversion of system energy into heat.
Friction and Damped Vibration
coefficient of friction (r)
a unitless number that describes the resistance to sliding of two surfaces in contact with each other.
Friction and Damped Vibration temporal envelope (waveform envelope)
the overall outline of a waveform as it changes over time
Friction and Damped Vibration
minimally damped (underdamped)very little friction in the system
Friction and Damped Vibration heavily damped (over damped)
a lot of friction in the system.
Friction and Damped Vibration
critically damped system
the amount of damping that causes an object to make only one vibration and then return to its natural (neutral) position
Friction and Damped Vibration
coefficient of damping (a)
a measure dedcribing the relationship between the coefficient of friction (r) and the mass (m) of a vibrating system, where a = r/2m.
Friction and Damped Vibration
rise time
the time needed for a waveform to change from 10% to 90% of its peak value.
Friction and Damped Vibration
steady-state-time
the time period during which a waveform had a relatively constant amplitude.
Friction and Damped Vibration
Fall time/Decay time
the time needed for a waveform to change from 90% to 10% of its peak value.
Friction and Damped Vibration
transients
a short, aperiodic fragment at the beginning (initial transient) and the end (final transient) of a periodic waveform; a state of motion that lasts only a very short time; it is normally seen after setting a system into vibration and after removing the driving force from a system.
Forced Vibration
driving frequency
the frequency of an applied external force
Forced Vibration
resonance
the state of a vibrating system in which no external force acts on the system and the system vibrates at its own frequency.
Forced Vibration
quality factor (Q)Book:
The lower the curve, the less responsive the system is to external forces. The narrower the curve , the more SELECTIVE the system is in response, in other words, the narrower the range of frequency at which a system can be forced to vibrate with large amplitudes. The selectivity of a system is commonly expressed by its QUALITY FACTOR (Q).
graph on page 65 of book. page 30 of notes
Glossary:
the ration of the center frequency to the band-witch of a resonance curve (response) curve of a system.
magnitude
the quantity or extent of a property of an object
compliance (C)
the inverse of stiffness (K); that is C=1/K
damped vibration
the vibration of a system that involves some damping.
damping
the effect of friction on a vibrating system
periodic motion
a motion that repeats itself in regular intervals
phase shift
the relationship between the phase of one waveform and another where one is considered as the point of reference.
Forced Vibration
resonance curve
a function showing the dependence of the amplitude of vibration on the frequency of the driving force.
periodic vibration
a motion that repeats itself (a vibratory motion in which an object returns to the same point in space periodically during the motion.
