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so far
we analyzed
calculated the periods of lots of also latest endurance
sprints
rollers hula hoops
we gave them an arctic
more the baltic librium and then they were also leading
at their own
preferred frequency
today at one of his groceries you what happens if i force upon the system
a freak until bio
so we call that forced
ulcerations
baker spring system
as we had before
exit polls are open
zakat
and we have the spring force
very familiar
minus k x
but now
these objects here which is mass and
are going to
bad before storage
i've zero which is the amplitude of the force
i'm to co-sign
will be getting so i'm going to
forces in a sinusoidal fashion
with a frequency
that i'd choose
this week and she is not the frequency with which the system wants to also
great
it is the one that i choose
and i can vary that and the question i was what real the object of
morton's second law
an eight
equals minus k x
plus but of course
at the wrong
cosign on an airplane
phase x double dot
sort of x double dot
plus
i've been using them
k over emb
times acts
equals f zero
divided by m
article time or reduction
now the question is what is the solution to this differential equation
very differently different farmers so before because we before we have a zero
two
now we have your driving force
it's clear that if you wait long enough that's a little later that system will
have to start also maybe
ebbets frequency
in the beginning
it may be a little different in the beginning of may want to do its own
thing but ultimately if i take you by your information q back-and-forth
in the beginning you mailed check but sooner or later
you will have to go with the frequency that i force myself upon
and when we reached that stage
recall that
the steady-state
as opposed to the beginning
when things are a little bit confused which we call
the trends in space
but in the steady-state
object much somehow must have been a preconceived
which is the same as the driver
i did have some amplitudes eight
and i want to evaluate the judith empty today
so this is my trial function
but i'm going to put into this differential equation
x dot
people's mind is eighty
omega
signed on may fifteenth
x double dot
equals minus any
omega spread
co-signer make it
until i'm going to substitute getting here
so i'm going to get mine is a day
omega scraped
co-sign only dot t_
plus
k over i a m
anxiety
cosine
omega t
and that he calls
af zero divided by m
articles on
oklahoma dot t_ and that was always hold
so therefore
i can
divide out michael title nicotine
i can bring the age together
so i get eight times k over emb
binders only got scraped
equals
af zero divided by m
modest ko crab
is something that we're familiar with
it we've got a system that we don't think we bring it the way from
equilibrium and we don't drive it
and we know that all the best quiet
which i will give a zero
people's ko grant
visiontek requested that we have dealt with before
this is the driving frequency is very different
and so i'm going to substitute in here
okay over ammo because it was clear
and so i find and that the and future app of theirs all jacked here
at the end of the spring
at zero
divided by m
departed by
omega zero spread
mind omega script
and this
and the germans
was very remarkable
directory sticks
for civil
if i
drive-thru system
had a very low frequency
sorted omega is much much more than omega zero
recall only go zero often the natural frequency it is the one that it lacks
if you have only got much much less than only a zero
discourse only got zero spread the scale for m
so you get an update judy
which is at your own
provided by kate
if you go only gotten duane above the natural frequency
let's say only a goes to infinity
becomes very very large
then downstairs
becomes very very large so it goes to zero
about what happened but on the back
is exactly or make it through
then the system goes wacky
look what happened the downstairs becomes zero andy amplitude goes to
infinity
and that's what we call resonance
active replied that at that frequency
the system ghost completely the sir
i can make a plot of areas of function
of frequency
when i say omega you can always always change too
perhaps if you prefer that the president may dot
used to buy princess so you can do with it and retreated to the rate is per
second
so if i make a plot
of the
amplitudes
versus frequency omega
then at low values
i have you ever zero divided by kenny
is the and picture
when i get the
resonance frequency the natural frickin shilpa system
it goes out of hand
goes to infinity
the moment that omega is larger than omega zero noted that the amplitude
becomes negative
a negative attitude simply means
that you get a all of us on the face change upon of eighty degrees
thirty object or some other eighty degrees are faced with the driver
i would not expand on that too much today but it is negative
and so it comes up here
and then proceed to general very high frequencies
of omega
so something very spectacular is going to happen
at the
resonance frequency of the system
in practice
of course the amplitude will not go to infinity
and the reason for that is that there is always frictional some kind
there's always damping
but you get a very high amplitude
infinitely high
so if i make you a more realistic plot
off the amplitudes and i will take now the absolute value the magnitude so we
don't have to worry about it getting
negative we don't have to worry about that one of the eighty degree
they shift
then you would get a curve that looks like this
and hear that
if this is frequently acts
thank you you would get
the natural frequency when things go out of him
and depending upon how much do i think there is
this curve
would look either very narrow very spiky
was very very high
and there's very little damping
or if there is a lot of them thing in the system it's more like this
and there are these
gold is the residents could have been narrowed it is
everest's
i have here a system
on the air track
which is an object that i can drive
was a free considered i can choose
here is a spring
object mass and
he is in the spring
abt fixed on this site
right there
and yeah i'm going to drive it
what have you this
variable force that you see there
and what i want to show you how is the first idle
driverguide a frequency
which is way below the resonance frequency
then you will see
but amplitudes not very large
i will then drive that way about the resonance frequency again you will see
olympics route which is very little if i can go very high frequency
duplicated almost and still
and then i will try to get the resonance frequency
and that's will be uh... it's about wong groups the residents we could see if i
just let these objects
we don't think
does this
now you see the natural frequency survive on earth
but now i'm going to drive it
here with the system
every going to put on this
was if we could say that we control
let me start
you see here the frequencies you indicator
very low
way lower than one births
and when you look at the way that the system response
if you wait long enough when the transients died out
you will see that they go hand in hand
but the amplitude
is inflation is the driver
that's why we have plus and the computer
the faces not so important today
which is a go hand-in-hand
very small amplitude
roughly half zero divided by kate which is to speak on simple to spring
now all the way about the resonance in the system both superior
so don't pay attention to the
there are any more
way above residents
pcx toxicity
look at the amplitude very was very small
when we went over this car
so first we probably can't
another prominent here
locked almost not moving at all
almost identical and wanting to be i've taken to now
and i'm going to find you
this reference which is the one who works
which is some way here
fairly high amplitude three not careful
then we can actually break the system
fairly high altitudes and try to scan over it now
go a little bit off resonance
bomb back on residents
she'll use at the gym
but it's a lot
so you see it a response
when i brightly system
when my system is a little bit more complicated
for instance
if i had
too much this year
so i would have long
spring constant k
clean constant k
i could repeat his experiment
if i get that
i would find to resonant frequencies
and if i do agree three objects i don't find three resident
i did was five i would find five resonant frequencies
and when i make then this curve
overage
amplitude
as a functional frequency
yeutter groups ordon radians per second whichever you prefer
that if i get
three objects their in a row
it which is something like this
and depending upon how many of these objects you have
more and more residences
i_d_'s residences can all be trumped by driving the system
and searching for them
if i go to a system
robot i have an infinite number
all of these
masses we call them coupled also latest he's also there is a couple to his
friends
an infinite number of coupled oscillators
would be a violin strings
is a violin strings
and the reason why i call it infinitely number also
also labor's is that
i can think of each animal he's molecule
as being driven
as being connected by springs to the neighbor
and sort of infinite number of couple postulates
and so when i start to shake this system
i would expect
a lot of residences
and that's what i want to explore ways you know
in the case here
that's the objects moved in the same direction
all displaying i called is the wider action
and i called the extraction thirty spring is in the actual election year
objects debate site in the excel rection
and also rations are in the extra rection recall those
longitudinal
uh... also mentions but
there's also a way that you could have transfers also asians
transverse
whereby the motion is in the white election where's the pizza in the act of
action i could even though did with this system
i could make them also late like this
because the springs who obviously also work
if i do this with mrs
and that's the way
i won't this
the violin string or play piano string
two also a towel because that's the only meaningful way that i can
naked oscillate
and so
i wonder if i'm going to
driving coupon shaking it up and down
searching for the resonance frequencies
i will be
that i thought very low frequencies the string
laughs at me to string does nothing
borat
doesn't respond to me
i am somewhere here
the residents could
but i'm gonna increase the frequency slowly i get to the very first
frequency at which it likes to also made a court of law
and when i look at this spring that you will see that shortly
the string will also might like so
will go up here
and it'll go down
and all it will do is this
should that's his first residents
and i call the zen equals mom
often called the first
then i go to higher frequencies
it will not do very much very unhappy
and then all of the southern
i hit the seconds
residents
i call that attitude
and the second resonance
will show up like this at this point of this strangle not move at all
when this part is up
his part will be done
nicolette s an equal split
and it also looks like so
and this point which is not moving at all week eleven no
i go a little bit beyond that
second resonance
and nothing happened to the spring to strangle be quite unhappy
plot was a little bit until i hit the ball residents
at st
and then
the max resonance
i will seek to elves here one here
and one here
mystery will also make like cell
this goes up and down
another eighty degrees out of space
and these two ends
in space
and an equal footing
and i can go on like that and add notes
and
i will show you some of that
very shortly
frequency that i generates
i call that apple pie and an is an integer kabhi balm
three or four
that hereinafter mo
in other words if you have a lot of work on that hurts
that have to
could be two hundred parents
and have to read
cpl
would be three hundred troops
recall any calls while
recall that the first couple nick
some books also call it the fundamental
i will call it the first harmonic
and recall any postal
the second harmonic
and song an equal three
is the spirit for a moment
so we're going to get a series of this screech frequencies
which were equally spaced
f_-one
depends
on the links
of the string
on the tension
i will write tension don't confuse these words periods
and it depends on the mass of the street
without going into the detail how dependent is decided
parameters that determine
i had he had a very special
violent string work piano strings whatever you want to call this
and we can generate
residents weakens his body
searching for them and i would need assistance from
student which'll be willing to help me
so you hand and mum
hold one end of the
piano string in your hands
don't let it go please don't let it go
i promise you i won't let it go either
okay so i put a certain pension elite
and i start to shake at a very low frequency
no carlo
look all that because
strenuous nothing
just laughs at me ignores me
doesn't like
not going to increase the frequency
nominating the first resonance coming up
eddie's
that's exactly the shape that you see on the blackboard
very clear
shake it here
have exactly
the residents
let me now try to
hits the
second harmonic
if i go up a little over the
f while men
nothing much happens
hard for me to see is this
here's the second como records of the twenty two thirds
already difficult
the thing that i think that the second
i think i got it now
okay sir do you see the second permalink
cd did note that point standing still
the amplitude as you know i was that's a correct respect for
residents with to recall also normal more frequency when natural freaked is
all the same thing
let me know try to generate one that is very hard times i possibly can
you tell me which
harmonic it is
all you have to do is count how many nodes there are not counting my hands
and his hands
and you add wild
and that is the
from only that i generate
system is not too happy to see you feel it sort of when it comes and
uh... akiyama or present
very hard for me to get resonance but
i will get it
there comes that there's no question that
dot i'm all right i don't know about it
carly simon residents
so how many to count
six hamanaka
look twelve to me that okay you come better than i can
okay thank you very much so you see here
power system response
through the driver
and a complicated system like this strength
has many many
of these resonance frequencies
which we called the normal moz
now when you have any
violent
your four strings
they all had the same length
their musical instruments like a piano will buy diamonds is different
violent four strings all the same length
sappy
tension so you have something to play with
tension is change normally when you tony instrument before you start playing
but these four strings all have a different max
and that gives him a very different frequencies
not to play the violin you cannot change the tension of course during the playing
that would be a bill difficult with all their instrument that exists
were actually
the plane depends on the pension maastricht
there's a violin that's not the case was a violent
the only option you have all your playing it is to make the
streamlined shorter
and you do that by moving your finger
along the street
by making it shorter
the frequency goes up and by making it longer
the frequency
goes down
now how do you excite
a musical instrument like a piano string or violin strings
there is nothing that is driving it exactly at that residence because if you
want to get a four hundred forty
where it's out of a violent street
then you not driving at exactly at the four hundred forty trips like we are
doing
well that's true
but if you take a bull
and you're up to string was a ball
that in a way what you're doing is you're exposing that string
to a lot of possible frequencies not just one
these are robbing action
i could also rob it was my finger wycliffe pluck it
why could kick it
and what it does it's it ignores all the frequencies
which i'm not at resonance
but it picks out the wilentz which are addresses
so striking it was a bow is effectively exposing it
to a hallmark spectrum of frequencies
and he picks out the ones
that it likes
in fact if you strike violin string was a bull
you may excited
simultaneously in the first public
and in the second and even in the third come on iq or even higher harmonics and
that makes the difference between the various instrument that gives it a
special
don't quality
depends upon the cocktail the combination
of the various
harmonics that you excite
now if you go to woodwind instruments
and the situation
quite different
i have here
assigned cavity
soapbox
has legs l
and there is a ringside
and i want to see whether this
system has resonance frequencies
so i put in here a little loudspeaker
generates
soundclick different frequencies
and search for residences
and there are
the residents of this system however
a different from this strength in that sense it's not the box it will resonate
here
but as the air itself that starts to resonate air acts like this swing
in fact in that sense it is very parallel to our spring system
it is also longitudinal
also they should where that is that france was also they should
so you make pressure waves in sight
and if you go to get the right frequency the air acts like a spring and then
strong reactions which are
the residences
in this case
and smoked
ends come on lick
is given by the m
times the velocity of sounds divided by two l
envy
it's about three hundred forty meters per second
at room temperature
so it is the sound speed
nor does it again later in the end
notorious given instruments
produces the certain
frequency
uh... let us say that l
close friend farsightedness
and you can calculate the frequency of one you know what the speed of sound is
freedom the forty
okay unequal swamp
so if we can see that he will get
equal three point forty
divided by two l which is no point five
needles
and sort of disney six hundred any difference
so did we did this big we could use six hundred eighty three x
but the second
among the cast too
with a double that
so we'll be thirteen hundred and sixty percent to what
now this
system which is close on both sides wouldn't be very good musical
instruments because you sound would not come out
so what people do they make them open
uh... sound cavity
which it is open on both sides
like this for instance
open on both sides
and even though it may surprise you
if we put a little
loudspeaker here
we can excite the air colin even in his own consistently to complete some other
way than we do with you to disclose system
and we get exactly the same
series or frequencies that i put you on the back
there also musical instruments
which opened on one side and close on the other
so this is called an open open system
and it would be cool close open clarinetist coastal
yeah i can also get to resolve
resonance frequencies even though here the series wouldn't be exactly like this
it's a little different that doesn't matter about how different but it's
it is a little different
but you get again the whole series
all residents frequencies
so again you see that it might make the system longer
i get lower frequencies
if i make the length
while meter
a big
then i would get a frequency
obama
which is about four times well within the one that i have there
which is from the seventy births
and if the second harmonic within three hundred
appointments and so on
so when you see him oregon
in a church you see all these organ pipes
different lengths that one month to promote owns
and the short ones at the very high price
and that is the way that these
instruments work
i have here
they
recording which
i have demonstrated to you before it is open on both sides
and because it is corrugated
in a very special way when i blow we pass this
it bill going to
residents that's to say
wind shear is like a spectrum of all possible frequencies
it's like the bow on the violent
and then they picked south africans is that it likes
however if i think reached a speed of the release
i can try to
force it into higher frequencies
so it'll always speech
are more likely to get
the were a lot more mixed a tyrant speeds are more likely to fifty
hyperbolic this one a seventy five centimeters long
it's open open
and if i were able to its peak
first harmonic
that would be a frequency of about two hundred and
forty hurts
i may not be able to excitement was for a moment
the first come only but i'll try but certainly the higher harmonics are very
easy to excite
and i can make you even this and simultaneously
to more than one frequency
just like the violin strings
strike it
and simultaneously also late
in combination of these mods
but this world is around
for start lowell
fees may be afforded
definitely way higher
uh... words is the most persuasive
for someone like
we're trying to do you think you could
simultaneous
jorwar
if you play a fruit
due to the following
make holes in here
and when you take your fingers elbows holes
then the effective length of the flu
if this law you get a high comm
you put your finger on this one
and effective length of the fruit is this what you get a little
you put your finger on both
effective length
of the flute this long
and you get an even lower
i have here a very special from
open on both sides
you see the two holes
will first closer to home
but this is the lowest frequency
well o'rourke
troops
which is a battle creek inn in someone's longer
i have another example he open instrument
treatise
over here
and here is trust
this is my version of the trombone
this figure
so it is a system that is like this
but i can move isn't
and so when i headed client
frequency would be height
united here
which is directly related for their legs
of this trumbull
and if you learn how to play you can try to play
the
it it
it into
it with the to b
it
it the
references
by all around us
when you drive your car
you may have noted that all of the southern you get some crazy rattle
somewhere could be your merit could be something else could be an ashtray
because you're driving it to your exciting it was the frequency would be
too real to go around
ueda residents we could see
yugo title slower
and the rebel stops with something else we start over
the reason why
the press metal stop because you go over evidence
but you may go on residents of another
objects that you have in your room
have preferred resonance frequencies
wedded to the other parts of the fans are what does your refrigerator or
anything you can think of everything
resonance freak because your body has residents weakens his if i took your
might
hands and i would start to shake you
then if i do it at low frequency
not much what happened but that would be one three three three two arms begin to
move like this like
their physical pendulum trite
and if i hit that frequency then indeed that would be a strong response until
your body has many
residents free contrition arms or legs
your head
everything
but also experience all of us emotional
residences
small imports
huge out
falling in love
is an emotional resonance
if someone purchased a
sensitive nerve
that these a
resonance someone could say something to you
it'll be fascinating issue for you and hugo normally here your response was
unbelievably strong
in my view
is also a forum
of a
emotional
residence
i have here to tuning forks
and these two reports i designed in such a way that all i would have to do which
is bangor
and they will pick out their own resonance freak
forty four
very simple like this
i give a ticket
and to keep his like dumping the whole spectrum of frequencies on its and it
picks up the ones that it likes
which is this one
and that's the one in vertical resonate it's possible that i can excited at
higher frequencies of higher from onyx but that's a little hard even with the
food court
so this one is two fifty six words
the prongs move two hundred fifty six times per second
and this one is form the forty carats
uh... you know overtones don't hear higher harmonics
it'll take something as simple as a wine glass like this
it has many many normal mode frequencies many residents frequencies
the lowest one is very easy to excite and i will do that i will robert was my
finger
robbing is like striking a string visible
all the same hikes posted to lots of free creatures it ignores double picks
out the woman it likes the residents we could see the normal mode
the natural frequency
and what the glass will do it it's lowest
harmonic in his first harmonic people sort of also went like this and i will
show that to you later in this lecture slow-motion
let me first
make you listen to the
the frequencies around four hundred inserting seventy percent of the wash my
hands because i have chocolate my fingers
and because of the trial
i will not be able to excited to have to be here others
with some liquid
therefore my hands have to be
shocked free
chalk is just
to greasy
try
i remember when i was just a little with my order
we were all the way
fidelia
and they thought
we cannot not exciting it was before the seventy fifth
and dumping the whole frequency
the whole spectrum of frequencies on it
and it picks up to one
that it likes which in this case is the four hundred seventy please
residences can be destructive
and rumor has it
that there are singers
women who play cat
align glass
and they do exactly what i did
listen carefully
degenerate get reconsiders their voice increased the volume of the voice and
then the rumor has it that ***
the glass coordinator with the and pictures of the blast
become so much
that you get so i feel close to
residents and so much
power goes into it because of the volume of the voice
that the glass
i'm going to try to break a class with you
and you'll see that it is not easy
i have here
wine glass almost the same as the one i have heat it there
and weekend illuminate that glass was a strobe lights
which you see here
and i'm going to show you there
the display
of that strobe lights and the reason why the strobe it is
that we want you to see as we excite the exact frequency
off the glass
we wanted to see the motion of the class and the way we can make you see the
motion is by stroking it not exactly at the frequency of the songs
but a little bit different free
so you will see the
strobe risco pick motion then
so i can
already i will make a darker shortly but i wanted to see at least
most of this bike and
generate then the
four hundred and seventy per which which is very close to the resonance frequency
as if it's going to be with you us
will increase the volume and then we will try to get that residents just like
we may be all piping works
we have to be white owned was in the roots
and then we'll see where we can make the glass break
i want to warn you this all is going to be very strong
so you made
as the time goes on as we go to higher volume you may want to turn
you may want to closure is in fact i won't use this
to protect my views
i'm leaving uses to protect my eyes in case the glass might break
which i doubt whether it will who knows
all right so let's make it very poor
so you see here the glass
not doing very much
and i'm not going to increase
the for two more personal
i'm going to cover my ears now
we didn't see some motion
i'm not sure that i won't residents
it all
it all
well the
understand that
residences can be very destructive
and there are some striking examples in history effectively of when there's a
storm you may have seen the traffic signs
this deciding on a poll
but the traffic sign stars doing this
this is straight because there's a wing to wing it is like a spectrum of all
kinds of frequencies
it's like growing eventually musical instrument
this traffic scientist exiled to treat consider that likes
and then if the reader strong enough
it could be very destructive in the most x trekking example of destruction
is that of a bridge which was built
and that is the calm of rich
the west coast which is very dramatic
and of course i will have to show you that movie you'll see what the wind can
do to a
so will start this movie and then we'll make it dark
first of july nineteen forty
delegation of citizens met in washington state
the weather was beautiful
the occasion to start
and the speechmaking fanfare
altogether appropriate
this was the grand opening
of the diploma narrows bridge
from the beginning
the bridge which ban puget sound between seattle tacoma
struggled and stuff
as well it should be
the diploma narrows bridge
was one of the longer suspension bridges corner
and if somebody had to overlook some
it probably would have remained
one of the longer suspension bridges on it
wasn't that break from the beginning
a lot of people didn't a lot of attention to detail
but somewhere along the line
and this was obvious man
it looks as if someone forgot
the significance
tacoma narrows bridge was the most spectacular alien harbingers
unfortunately its first performance was destined to run only about for months
in the meantime
she was a beautiful bringing
but a little strange
even before construction is completed
people observed is peculiar behavior
that was because even and light breeze
ripples ran along the bridge
after a while
one of the local humorous colour galloping dirty
and for fairly obvious reasons named scott at least until the seventeen
million nineteen forty
and now
seattle tacoma were sports minded cities
for four months original sport was to drive across the bridge on a windy day
well some claimed it was like driving world
others down into little disconcerting to see the car in front of the severe
how popular this bridgeport was or to what extent it might have spread across
the country is anybody's guess
on november seventh nineteen forty
the winds were relatively minor
about forty miles per hour
unmoved beer
rather than red
ridge begins wednesday
mine
and leavening
facing what's residents could do
with musical instruments
we're stuck with it
speed of sound working for him before he makes perfect
and when i speak to you
i have here they sound cavity
which has a certain size of certain shape and while i speak
this size in this case justice
size and shape changes all the time
and that this might force a very characteristic songs makes it possible
for me to make a blow some makes it possible for me to make up myself
and whether how i speak
it will say yeah yes no question that swath of the word that's clear very
recognizable each one of you and i at the very well recognizable voice
the situation will change
i could change the speed of shops
in my system
helium
which has a very different molecular weight from air
has already higher speeds
then the
speed of sound in there it's about to point seven times higher
two point seven times
three hundred forty meters per second
so if i tell my system with helium
barred from the fact
that there's no oxygen evening so i wouldn't survive very long that's a
detail
if i told my sister with helium
of course my vocal chords and lifestyle cavity here
they don't know that so they do the same thing that they normally do when they
speak to you
however since the speed of sound
is much higher here in my cell cavity if we could see that it will produce is
very hot
i some very different
they're probably operates as i mentioned there is no oxygen in here and yet if i
only take about a bit of helium doesn't work very well and you don't you're much
different so i have to really take a lot of him
and i'll try that
but that for that i've been a small price
and small prices that
you confront
apply just to stay away from the fainting level
for viewers helium
i have to let my hair out first and then get a demand and may be that the helium
out again and that the union in the dead and during that time i i can't speak for
then but i think i'm for enough was helium
so you can withstand
for that kept the pressure up to level that i like
huh
well character a profound bharat wilco well i hope you enjoyed it and i feel
that they think you