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PROF.
WALTER LEWIN: I have here a system on the air track, which is an object that
I can drive with a frequency that I can choose.
Here is a spring, object, mass m.
And here is another spring, it's fixed on this side right there.
And here I'm going to drive it, so I have here this variable force
that you see there.
And what I want to show you now is that first I will drive it at a
frequency which is way below the resonant frequency.
Then you will see an amplitude not very large.
I will then drive it way above the resonant frequency.
Again, you will see an amplitude which is very low.
If I can go very high frequency, you will see that it almost stands still.
And then I will try to hit the resonance frequency.
And that will be-- it's about 1 hertz, the resonant frequency.
If I just let this object do its own thing--
just this--
now you see the natural frequency.
It's about 1 hertz.
But now I'm going to drive it here with a system and we're going to pull
on this spring with a frequency that we control.
So let me start.
You see here the frequency.
You see an indicator.
Very low, way lower than 1 hertz.
And when you look at the way that the system responds, if you wait long
enough when the trangents are died out, you will see that
they go hand in hand.
That the amplitude is in phase with the driver.
That's why we have plus amplitude here.
But phase is not so important today.
You see they go hand in hand.
Very small amplitude, roughly of 0 divided by k, which is the spring
constant of the spring.
Now I'll go way above resonance, and this system will slip here.
So don't pay attention to the arrow anymore.
Way above resonance.
You see it starts to slip.
Look at the amplitude.
Very modest, very small.
But we went over this curve.
So first we probed it here, and now we're probing it here.
Look, it's almost not moving at all.
Almost standing still and I'm driving it with high frequency now.
And now I'm going to find you this resonance, which is near 1 hertz.
Which is somewhere here.
And look, very high amplitude.
If we're not careful, then we can actually break the system.
Very high amplitude.
I'm trying to scan over it now.
Go a little bit off resonance.
Now I'm back on resonance.
See what a huge amplitude.
That'll turn it off.
So you see here the response when I drive a system.