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Discussion: Simple Harmonic Motion tool
Topic: Simple Harmonic Motion (SHM)
Related Item: http://mathforum.org/mathtools/tool/1127/


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Subject:   Response to Sione
Author: Craig
Date: Feb 5 2004
When I said "function flyer" does the same thing, I was referring NOT to your
applet, but to the one Steve mentioned.

It is possible for simple harmonic motion to result in values not symmetric
around zero--it just depends on initial conditions.  For instance, a
spring-mass system may count equilibrium as the zero, yielding y=a*cos(bt+c);
if the floor (or hangpoint of the spring) is counted as zero, then you get an
additional (constant) vertical displacement.  Think about the rider on a ferris
wheel--probably more concerned about her height above the ground than her
vertical displacement from the central axis of the wheel.

Modeling height of a ferris wheel rider using simple harmonic motion is
accessible to algebra 2 students who may not be ready to handle the
relationships between position, velocity, and acceleration--more in terms of
describing what they see, than trying to explain the physics of the
phenomenon.

On Feb 04, 2004, Sione wrote:

No, it is different. The one that you described "function flyer" is a function
plotter, although you can plot an SHM as well as any "sinusoidal" function such
as "sin(x)" , "cos(x)" , blah, blah , blah.

>you simply type in something like "3*sin(1.4*(x-2))+1" >as the function

The function you described "3*sin(1.4*(x-2))+1" cannot be physically (Physics)
possible to be called as SHM since the  max displacement is "+4" (ie, 3+1) to
the positive direction, and the min displacement is "-2" (ie, -3+1) to the
opposite (negative direction). Have you seen any pendulum (real physical SHM)
that swings past the vertical line (equilibrium position) to the right (positive
direction) by say 15 degrees and swing to the left (negative or opposite
direction) past the vertical again only to 10 degrees? SHM Physics does not
happen this way. It the pendulum is displaced by say 15 degrees to the right and
released , it will swing past the vertical to the left and reached a max of 15
degrees. That is they are both the same in either direction.



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