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Re: displacement and graphs



At 10:22 AM 10/9/01 -0600, Larry Smith wrote:
Does the term "displacement" refer to the vector r (from some arbitrary
origin)

Yes. That's the general idea.

or does it refer to r_2 - r_1 (i.e. final - initial). They are
clearly not the same thing but it seems texts use "displacement" for both
concepts.

They are closely related concepts. The latter is a special case of the
former, namely the case where
1) we assume the arbitrary origin is the initial position, and
2) we assume all we care about is the final value of the displacement.
Sometimes the two foregoing assumptions are obvious from context; if not,
they must be stated explicitly.

Other assumptions sometimes make sense. For example:
-- If somebody is asking for the displacement graph, assumption 2 is
obviously !not! in effect.
-- Suppose you have an array of mechanical oscillators. We might define
the displacement of each one to be its position relative to its own (!)
resting position. This will not, in general, be its initial position.