AP Physics - Experiment 2a

Using DataStudio^TM to Graph Experimental Data - Part 2

[Lab Index]

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Purpose:

This lab extends the previous DataStudio^TM lab in two ways:

you are going to analyze a slightly more-complicated situation, and
you are going to construct your own experiment file.

As in the previous DataStudio^TM lab, you will reanalyze data from a prior experiment - in this case, the "Period of SHM" data.

Discussion:

Back in the "good old days" (I know how you young people love to hear stories about the "good old days"!), when data analysis was done by hand - perhaps with the aid of a slide rule or table of logarithms - the standard (only!) way to do it was to find some mathematical combination of the experimental quantities that would graph to a straight line. It was just too much computation, even for the most enthusiastic young physicist, to do it any other way. Today, even though computers have revolutionized data analysis (among other things...), straight lines are still very important and commonly used.

In this lab, you will learn how to set up a graph, perform calculations on data, and graph and analyze the transformed data.

Equipment:

DataStudio^TM software

your data from "Experiment 2 - Period of SHM"

Setup:

Open the DataStudio^TM software. This time, click on "Enter Data" from the initial screen. You should get a screen like this:

You could just begin typing your data into the data table, but it would be more professional to customize the setup just a bit. Click the

button at the left of the main toolbar. This opens the Summary Window, which contains Data and Display panes. The Data pane lists all of the data sets generated so far (The data set A_data under Editable Data is data Table 1.), and the Display pane shows the ways in which the software can display the data.


The Data pane appears at the top of the Summary window. It shows - and allows you to access - all of the data generated in the experiment.	The Display pane appears at the bottom of the Summary window. It shows - and allows you to select - the ways in which your data can be displayed. You can change the name of a graph or table by clicking on it and typing the new name.

Double click the data set name (A_data) in the Data pane, and the Data Properties dialog will open. Here, you can rename the data set and the x and y quantities (with units). You generally don't need to specify minimum or maximum values for the data - the software will calculate them from the data you will enter. "Precision" in this dialog means the number of significant digits displayed.
Finally, click the settings button () in the graph's toolbar. Uncheck "Connect Data Points" in the "Appearance" pane (Aarrrrrggggghhhhh!). Then select the "Error Estimates" tab and enter the estimated uncertainties for mass and period.

Procedure:

Type your mass and period data into the data table. Note that the points are (again!) plotted on the graph, and the scale adjusted, as you type.

Results:

Now, you need to find the equation that best fits your data. You can try some of the functions in the menu (in the graph's toolbar), but I don't think you are going to find a really-good fit for this data from the given functions. Note: You may get a reasonable fit from "Polynomial", but this doesn't say much. Physicists generally scoff at a polynomial fit. This is because there is an interesting theorem in mathematics that says that you can fit a polynomial to any continuous curve (over a restricted domain) if you are willing to calculate enough terms in the polynomial.
The DataStudio^TM software has a "quirk" in that it will only do calculations on the independent (y-axis) variable - period in this case. We can't, therefore, plot the square root of mass vs. period - but this is not a problem, really. We will simply plot mass vs. period², which is logically (mathematically) equivalent.
Click the calculate button () in the main tool bar. (Note: There is also a calculate button in the graph's toolbar (), which works similarly, but not exactly the same. You can try it sometime.) The Calculator Dialog will appear. Select "pow(x, 2)" from the menu. Click the when your dialog looks like the one below.
If all has gone well, you will notice a new data set listed in the Data pane of the Summary window. To create a data table for this data, simply drag its icon from the Data pane and drop it on the Table icon in the Displays pane.
To create a graph for this data, drag the data icon from the Data pane and drop it on the Graph icon in the Displays pane. You will need to change the Settings () for this graph (uncheck "Connect Data Points", and set appropriate "Error Estimates").
DataStudio^TM does not automatically change the axis labels and units when a calculation is performed. To do this, press the button in the Calculator dialog. The Data Properties dialog for the calculated data will appear, and you can make appropriate changes (y-data is now "Period squared", and units are "sec^2", for instance).
Now, you can go to the submenu and select "Linear" (or "Proportional") to get a best-fit straight line for mass vs. period².
You can plot your data for other springs by selecting "New Data Table" from the "Experiment" menu, and starting over.

Conclusions:

As before, it isn't necessary to restate your conclusions from the original experiment (unless they have changed!), but what do you think about this method of data analysis?