Vernier Logger Pro Modeling, Fitting, and Linearization - Manual (Page 4)

Logger Pro Modeling, Fitting, and Linearization
©Vernier Software & Technology 4
analytic function. The reasons for this assertion are outlined in the following tables where we describe
how Logger Pro software can be used for mathematical data analysis.
A practice we especially want to discourage is telling students to “find a function that fits the data.” Until
students have a robust sense of how and why functions must be connected to physical models, they are
likely to choose functions that the instructor considers unsuitable. This practice also reinforces the idea
that physics is just a collection of formulas for special cases rather than a general framework for
analyzing nature.
Using Logger Pro for Mathematical Data Analysis
In the table below we outline specific procedures for three modeling methods, along with some Pros and
Cons of each method. More detailed steps can be found using the Logger Pro Help Menu.
Analytic Mathematical Modeling
Steps
1. Enter or record the data in Logger Pro.
2. Insert a graph of the two variables being analyzed (with Connect Points turned off
under Graph Options).
3. In the Analyze menu choose Model and then the analytic function you think will match.
4. Think about the physical meaning of each coefficient. Estimate the magnitudes of the
coefficients based on what you know about the experiment. If a coefficient cannot be
estimated, set it equal to 1. If the model graph does not match the data, either improve
the estimates of the coefficients or choose a different model equation.
5. Close the window with the small graph you matched. This displays a larger overlay
graph. If needed, make more changes in the coefficients.
Pros
1. Efficient modeling requires users to understand or learn the role each coefficient plays in
providing information about a physical situation.
2. Modeling (or manual curve fitting) is the best way to learn how each coefficient in an
equation affects the graph of the analytic function.
3. A skilled modeler can match sinusoidal functions efficiently in some cases that require
repeated attempts at curve fitting.
4. Envelopes of functions can be seen visually and modeled. For example the local maxima
of a damped oscillation can be modeled visually but not fit.
Cons
1. Modeling takes longer than automatic fitting, especially when there are coefficients that
cannot be estimated. It is tedious in projects where many similar graphs of data must be
analyzed graphically.
2. Modeling may not be as beneficial to users who already know how each coefficient in a
particular function affects its graph.
3. Although modeling can give users uncertainty estimates, finding a minimum uncertainty
is more tedious than it is for fitting.