Discussion:  Simple Harmonic Motion tool 
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Related Item:  http://mathforum.org/mathtools/tool/1127/ 
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Subject:  Simple Harmonic Motion (SHM) 
Author:  Sione 
Date:  Feb 4 2004 
I have written a similar applet (Mechanical Simple Harmonic Motion) in 2003, for
a demo by the New Zealand Institute of Physics for promotion of Maths to High
School students of how it(Maths) applies to Industry and Engineering
Profession. They use it as part of a presentation at a conference for
Professional Engineers and Math Teachers. The applet is an animation of
"SpringMass" oscillation (a spherical object is attached to a spring). Omega
('w') and the wavelength (lamba) is dependent on the Spring stiffness ('k'), so
the user can actually input the value for 'k'. The amplitude 'A' is chosen by
the user but it is independent on 'k'. I chose phi to zero, since it is logical
at high school level that you only look at the motion of the "SpringMass"
systems at t=0 (time), and x(0) = A, this implies that phi=0 when displacement
at time zero , x(0) is at maximum , that is 'A'. I might include a SHM for a
lowpass electronic filter circuit (resistorcapacitor) and bundle them
together. User can have input for value of Phi. Graphs is interactive as
displacement x(t) , velocity v(t) , acceleration a(t) ,
translation kinetic energy T(t) , rotational kinetic energy R(t) and total
potential energy U(t) are incrementally plotted as the "mass" oscillates. This
means that the user can see the wavelength and work out the quantity of the
physical observables as a function of time.
I still hold the copyright when I wrote the applet as I am an active promoter of
Maths to High School in New Zealand as well as industry (Industrial
Mathematics). I was not thinking that it would be relevant to MathForum since it
is a Physics applet. Since I have seen math related problems to Physics
frequently discussed here at MathForum I might as well send it to Suzanne
Alejandre(MathForum) to be added to my collections of math applet already
available here. I will make some modifications (and perhaps add pendulum SHM and
an electroniclowpass filter SHM, if there is no time constraint on my
part) and then sent the applet thru to MathForum. I guess I will let you know
when it is available.
Cheers,
Sione.
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On Feb 04, 2004, Steve wrote:
This simple harmonic motion applet is a really nice supplimental tool. Lots of
students get confused as to how phase shifts and wavelengths are expressed. I
really like the idea of being able to manipulate the graph by moving any of
three points. A helpful addition could be to have phi and omega in multiples of
pi, as well as the pure numerical values. Another possible idea would be to
allow students to type in values to see how the graph changes, in addition to
sliding the three points. I noticed that the graph gets a little strange for
very small wavelengths.
 
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