WEBVTT

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So let me summarize what
the steps that we've taken

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are to do this
differential analysis.

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So when you're trying to analyze
a continuous mass distribution,

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the first step is to pick
some arbitrary mass element,

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a small but finite
size mass element

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somewhere in the middle
of the mass distribution.

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You don't want to pick
one of the endpoints,

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because the endpoints
are special.

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You want to pick an arbitrary
point somewhere in the middle

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and then pick a small mass
element at that point, so

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a small but finite size.

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Analyze the forces acting
on that mass element.

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So write down Newton's second
law, the equation of motion,

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for that mass element.

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That will give you what the
forces are on that element.

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Then go to the limit of an
infinitesimally small element.

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That will give you a
differential equation.

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You can then separate
the differential equation

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and integrate both sides
to solve the differential

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equation.

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And then finally, you can
apply a boundary condition,

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something you know about one
or the other of the endpoints.

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And that will allow you to solve
for the function of interest

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at any point along
your distribution.