Physical Phenomena

(Created prior to 1993)

Question: Can you give me examples of simple physical phenomena that are not 
functions?  I can understand about discontinuous phenomena.  But what 
phenomena have more than one y for any one x possibility fory at any one x?
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Well, the simplest thing I can think if is a circle.  A circle 
has two y for every x, except where it does not have any at all (except at two 
special points).  If a circle does not sound like a physical phenomenon, you 
might want to explain how light works.  I light wave is a sinusoidal variation 
of electric and magnetic fields.  If x is the electric field value and y is 
the magnetic field value, they trace out a circle as time goes on.  In fact, 
many "orbits" are circular - for example, a plot of a harmonic oscillator 
(like a spring bouncing up and down) with x = displacement and y = velocity 
also will give you a circle.

Arthur Smith
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There must be thousands!  How about Lissajous figures from simple 
circuits?  You hook an oscilloscope up to two components of a circuit which 
are oscillatory in time and plot one voltage as x, the other as y.  All sorts 
of interesting closed curves result, depending on the phase difference and the 
frequency ratio between the two oscillators.  Also, there is the phase diagram 
of water...but there is no simple equation associated with that, I know.  I 
guess that I vote for the velocity (or momentum ) of a harmonic spring plotted 
against its position.

Topper
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