>> You know some time ago Jeff
suggested, according to that scheme,
that we have a specific model to address
or illustrate some mathematics
problems, particularly eigenvalues.
Now in my past I have had a
bit of exposure to eigenvalues.
The most famous being Schrodinger's equation
and all the solutions associated with physics.
But there are a lot of mechanics
and electronics problems as well.
I had a strong illustration
of that in October of 1989.
I was working on the 8th floor of
a building in downtown San Jose
when the Loma Prieta earthquake struck.
And the building I was in
started vibrating, oscillating.
And in my office there was a file
cabinet here, and a file cabinet here,
each with about 300 pounds of files.
This one opened, and then that one opened,
and this one opened, and that one opened.
Now I didn't say I'm living in an eigenvalue.
I said how do I, how do I get out of here?
But, the vibrations of mechanical structures
like bridge, is a mechanic's problem,
that it can be addressed by eigenvalues.
This specific one started with the
idea that's in many textbooks which is,
spring mass, spring mass, spring.
And that could be illustrated in
classrooms if we we have an air table.
So Jeff said, can we illustrate
an eigenvalue like that?
But, it must be cheap.
It must be so cheap that any
community college instructor anywhere
with zero budget can build it.
So the challenge was, how do we do that?
Leaping a couple of steps,
we said well a pendulum
in small angle oscillations is like a spring.
So if we have a double pendulum, that is
two pendula that are coupled by a spring,
mathematically that's about the same.
In fact it's exactly the same mathematically
if we keep the oscillation small.
And the question is, now that we can
build that, how do we measure it?
So we were lucky enough to find some free
software that was developed at Aptos College,
the name of the college,
community college over in Aptos,
Cabrillo College by now a retired
physics professor called Tracker.
Tracker is free, it's downloadable and it can be
used to analyze any type of mechanical motion.
What it has is frame-by-frame
grabbing of a video.
And then you can track any feature
in that frame, frame-by-frame.
So by building this apparatus and getting
my cheap camera, that's several years old
and putting it up here and
looking down, we could take a video
of these two masses and then have a target.
Again being cheap, this is a
used CD with the label on it.
And we can then track the motion of the
black dot, in some of the other things
that Jeff shows we'll see that motion.
And then we can do a frame-by-frame analysis and
put the results of that position measurement.
And then by subtraction,
the velocity measurement,
or the acceleration measurement
into a spreadsheet.
And then by analyzing that spreadsheet,
or simply displaying the results,
we can have an eigenvalue
problem we can get our hands on.
So, what happens when we get this vibrating?
What do you think the most comfortable
modes of oscillation, or the preferred modes
of oscillation, the so-called
German eigenvalues are of this?
Huh, well there are two.
Both moving together.
And this is simply a child on a swing.
What's the other one?
Opposite. But what happens?
Now this one's moving.
Oh no that one's moving, but this one is still.
Now this one starts to move.
Okay. So now in the linear algebra course,
you say, how in the world can we analyze that?
And then if he's sitting here, linear algebra.
The rest is mathematics.
