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Discussion: All in Calculus
Topic: tool: Scatter Plot Applet
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Subject:   ScatterPlotApplet
Author: Sione
Date: Feb 9 2004
Steve,

Try this applet for "Polynomial Fitting" (least square estimates) where you
enter the data pairs , ie, "x" and "y" into a table , then specify the
polynomial order which gives the best fit. If you specify order 2 (square) it
will give the best fit for coefficients of 'a', 'b' and 'c' :  

 y = a*x^2 + b*x + c

If you specify order 3, then the best fit coefficients will be calculated:

 y = a*x^3 + b*x^2 + c*x + d

The maximum order you can specify is  10. You can also input any value of "x"
and it will tell you the approximate value of "y" according to the polynomial
order you specify:

Applet is found here:

http://mathforum.org/te/exchange/hosted/palu/polynomialftting/PolyFitApplet.html


Like you mentioned, it would be useful for physics & chemistry. Two experiments
that comes to mind are:

1) Measuring gravitational acceleration (gravity) by using a swinging pendulum
(simple harmonic motion). The student can measure the length of the string which
attached to the pendulum and the frequency (swings) of that specific length. A
table of different lengths can be plotted against corresponding frequencies ,
where the slope and intercept are use to solve simultaneous equations to find G
(gravity acceleration).

2)The second experiment is stretching the length of an unknown spring constant
of a spring with different force (weight) strengths. The force strengths(mass
times weight) can be plotted against the amount of stretching (displacement from
equilibrium), where the best fit slope is the spring constant ('k').

Cheers,
Sione.


==========================================
On Feb 08, 2004, Steve wrote:

http://math.hws.edu/javamath/config_applets/ScatterPlotApplet.html

This applet is very user friendly.  I like that it is easy to input coordinates,
and that different properties of the best fit line automatically show up.  This
applet has obvious helpful applications as a supplement to chemistry or physics
experiments.  I also like the fact that you can load in a data set.  The only
thing I didn't see is if you can alter the best fit line.  Can this line be
altered to properly fit data that follows a square or cubic relationship for
example?  If it did, this applet would be far more useful.


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