Date: Around 1993
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?
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.
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.
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Update: June 2012