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[Music]
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how do you do ladies and gentlemen and
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boys and girls
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i'm julia sumner miller and physics is
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my business
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and our very special business today has
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uncommon enchantment because the motion
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is beautiful to witness
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and wonderful to understand
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we are going to talk about simple
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pendulums and other oscillating things
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consider the following
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if we have a rigid support and there are
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none really because everyone shakes
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however rigid
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and we hang an ideal string by an ideal
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string i mean a string that has no mass
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no weight has no inertia has no tension
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is perfectly inelastic ideal
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mathematically and we hang a small bob
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on the end
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and we displace it from this equilibrium
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position and let it go
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it oscillates as a simple pendulum
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now we wish to explore its motion
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when you study the lesson in this
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business
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you will find that
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the period which is the time for a
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complete trip comes out to be
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some such expression with which i will
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not have much to say about which i will
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not have much to say
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it's governed as we see by the square
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root of the length and depends upon
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where we time it
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you know for example the g is one thing
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on the earth and quite another thing on
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the moon
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g is 32 feet per second per second on
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the earth but about one-sixth of that on
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the moon
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as an incidental fact matter you would
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weigh therefore one-sixth as much on the
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moon as you weigh on the earth
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now i wish to do another pretty
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experiment
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with several
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pendulums and i suppose maybe we could
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say pendulum this may be the plural of
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pendulum now what am i going to do
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i am going to hang up three of them as i
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have them here soon to witness
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one
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two
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three
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and how long are they going to be this
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one is going to be 10 centimeters long
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and this one 40 centimeters long and
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this one 90 centimeters long so the
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lengths are 10
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40
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90 centimeters
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notice the numbers 10 40 90. i hope you
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get a little q in there there's one
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there's four there's nine if we divide
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each one by ten
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now i am going to set them into
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oscillation
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and i am going to count say 20
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vibrations of each one
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here's the way i would do it
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i would set this one into vibration
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starting with zero and here is a clock
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which i would start and stop
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and i will just run one a moment to give
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you the cue
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i would remind you parenthetically
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i am not really giving you a lecture in
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physics i am merely pointing out some
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things that you yourself can do with
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your teacher and even at home
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and my purpose is singularly this to
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invite your interest and stir your
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enthusiasm and curiosity
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and point up at the same time the beauty
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and drama in these things so i would
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start this
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zero
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zero one two three four and i would
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count 20 oscillations
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and what would i get probably in this
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laboratory i would get about 13 seconds
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now where you are say colorado on a high
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mountain you would get a different time
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and if you were in australia you would
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get a different time because little g is
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different from place to place on the
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earth so i count 13 or 20 oscillations
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and i get 13 seconds now i do it all
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over with this one
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and i count 20 oscillations and what
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would i get i would get about 26 seconds
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you're thinking of something
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then i would do it with the 90
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centimeter one zero
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one
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oh i should have stopped this thing
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because i'm not really clocking
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yeah what's going on here
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huh
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well there's something wrong with the
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notice now this is this is the hazard we
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run when we depend on mechanical things
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so i'm going to put the clock out of my
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sight what would i do coming back here
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somebody says isn't the professor having
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a wonderful time with things going wrong
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sure they are when you deal with nature
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you must make her requirements
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absolutely perfect or she will not do
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what you want done so i
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count
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i count 20 oscillations and lo and
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behold i get 39 seconds
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look
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10 40 90 they are in the ratio of one to
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four to nine
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13 26 39 they are in the ratio of one to
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two to three
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and now a marvelous thing is encountered
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one is the square root of one
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two is the square root of 4 and 3 is the
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square root of 9. and that's what that
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so-called formula says that the period
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is proportional to the square root of
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the length and this other stuff comes
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out of some mathematical gymnastic so we
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have learned a wonderful thing about
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pendulums by examining the motion of
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three of them
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now strangely enough
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when you make the exploration or develop
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the formula mathematically notice notice
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that it does not contain
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it says nothing about
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how big is the pendulum bob how massive
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is it
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all the period depends upon is its
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length and you can show this by such an
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adventure as i have here
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here i have some
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pendulum which are of identical length
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let us say
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here is one made of brass there is one
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of aluminum there is one of cork and we
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would find that if their lengths are
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identical then their periods are
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identical and that's a wonderful thing
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because wouldn't you think that the
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heavier the bob
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that
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a different period would result
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no it does not
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so we deal with simple pendulum
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pendulums a bob on the end of a string
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now anything can be a simple pendulum
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anything let me illustrate supposing i
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took you took me here there i am and you
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put a hook there in me and you you you
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oscillated me
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i am a pendulum but not a simple one i
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am a complex one
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or more more more uh better physics
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language i am a physical pendulum
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a physical pendulum
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and what is a physical pendulum
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anything that is not a simple pendulum
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illustration
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here is a metal rod
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now if i put this on a support
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at one end and i oscillate it
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in a vertical plane it has a certain
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period
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it has a certain period
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now remember if it has a certain period
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about an axis through one end
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it has a certain time for its
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oscillation
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must there not be a simple pendulum
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which has the same period yes indeed a
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simple pendulum
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has the same period if it is so long now
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how long is the simple pendulum that has
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the same period as this rod
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wonderful
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if this rod is length l
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the equivalent simple pendulum is
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two-thirds of l
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so if i had a simple pendulum hanging
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here
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in this fashion
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which was two-thirds as long as the rod
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and i put them into oscillation together
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they would stay in phase meaning that
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they would keep step instead
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so we speak of the equivalent simple
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pendulum as a simple pendulum which has
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the same period as the physical pendulum
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now this is a rod
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and this has a marvelous property
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if i turn it around
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and put
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it would be looking like this of course
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now
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here's the two-thirds mark
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here is a remarkable thing absolutely
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enchanting
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this rod has the same
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period for this axis
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as for this one
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the same period
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and hardly anybody ever believes that
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but it is true as you can get discover
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by doing the experiment yourself
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so now we explored a physical pendulum
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which is a
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rod
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how about a hoop
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here is a hoop
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i have here a hoop
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and i could support it by an axis about
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one edge
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and i could let it oscillate in a
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vertical plane
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i could let it oscillate in a vertical
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plane
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does it not have a certain period of
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course
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it therefore has an equivalent simple
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pendulum
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and how long is the equivalent simple
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pendulum it is a marvelous thing to
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discover but the equivalent simple
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pendulum has a length equal to the
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diameter of the hoop so if you put a
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simple pendulum up here
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which has this diameter this length
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they would keep in phase
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finally
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how about a disc
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oh a disc
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here is a uniform circular plate and
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could i not support it on an axis in the
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manner as before
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and let it swing in its own plane
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supposing well i better draw a new
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picture
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we are talking about a circular disk
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a uniform circular plate and i
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oscillated about one edge
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what is the equivalent simple pendulum
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strangely enough the equivalent simple
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pendulum is three quarters of the
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diameter a matter which you can explore
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by making some of these things yourself
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now in addition to simple pendulum
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that's a bob on a string
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and physical pendulum which are bodies
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of any shape like rods and discs and
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hoops and the like there are many other
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oscillating
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devices consider for example a spring
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here is a beautiful spring
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nicely wound
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uh so long when unloaded
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i put a load on it
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and i call your attention to the
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beautiful motion which it executes
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that has a certain period in terms of
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the property of the spring now supposing
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i put a heavier load on it a heavier
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load
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watch it
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and i say that's a beautiful motion to
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experience to witness
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and now
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the question a beautiful question here
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is a spring of certain length and so
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stiff here is an identical spring
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which is only half as long
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the question which arises is this
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if the motion of this pendulum is so
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much with a certain load
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what would be the motion of half the the
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spring with the same load
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and it is a wonderful thing to discover
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that it has
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well i'm not going to say i'll leave it
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as something for you to explore because
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i think it has much more virtue to leave
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some questions unanswered for you to
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explore than to just give you the answer
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so i suggest you get a spring indeed two
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springs
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and explore their motions when one is
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twice as long as the other and indeed
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you will notice that i have couple
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springs in different ways
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suggesting that their periodic motions
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depend upon how they are coupled
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regarding coupled pendulum look here
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here i have a pendulum a heavy lead bob
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on the end of a rod which is pretty
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nearly a simple pendulum and here is
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another one
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and i have as we say couple them
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by putting a spring between them
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and watch the marvelous behavior i'm
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going to start one
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i'm going to start one
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and let it swing
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and we will see this enchantment
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its motion will soon die out
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and the other one will take up the
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motion then that one will die out and
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the other one will take up the motion
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and this coupling of pendulums has much
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to do with electric circuits about which
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we shall talk another time but watch it
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this one is going
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that one is going more watch this one
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stop
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that has practically stopped
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now this one is going to stop
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it has practically stopped and this one
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is going and so we speak of coupled
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harmonic oscillators here is another
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pair here are two weights on very
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flexible rods if i start one
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we will discover a wonderful thing
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that the motion of the first one
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is arrested and the energy is taken up
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by the second one
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so
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i urge you to explore the behavior of
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oscillating bodies and i thank you for
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your attention
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[Music]
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you
