Physics Modeling: Chapter 2 Examples

The OSP Data Tool is used for analysis such as curve fitting.

Euler Falling Ball Analysis

A graph reveals much about the behavior of a model but the precision of on-screen measurements is limited. There are two approaches to obtaining better data analysis. We can program the analysis ourselves within the model or we can use a general purpose data analysis tool.  The Euler Falling Ball Analysis model introduces the Data Tool to analyze Euler's numerical method solution of the fall particle model.

Questions:

Run the model with a time step Δt=0.1to generate time-series data and click the newly added tool button to show the Data Tool. The table columns display the numeric and analytic solutions. You can change the tool's display by clicking on the style file above the data column. You can right click on the tab to create additional data tabs.

• Use the Data Builder in the tool to create a new column. Add a data function named error and click within the function's expression field to analytic-numeric.
• The Data Tool can fit the horizontal data and the first vertical data column to a function with unknown parameters. Select the fit checkbox and choose a parabolic fit and select autofit. Note that you can drag data columns into the first position. How accurately does the numerical solution fit the quadratic coefficient? The linear coefficient?
• Drag the newly created error column to the first position and fit the data. What polynomial coefficient changes when the time step Δt is decreased and how does this coefficient change?

Note that you can change the graphical display by clicking on the style field above the data columns. You can also right click on the tab to create additional data tabs and delete unnecessary columns so as to simplify the Data Tool display.

Online help for the Data Builder and for non-linear