v Introduction @ Here we present two data sets that will be plotted and then fit to various mathematical functions. @ 1. Consider the following two data sets: You may want to take a screen shot or a photo with your phone so you have the data on hand when filling in data tables later in this lab, otherwise you'll need to scroll up and down as you enter data. 0 In Part 1 you will plot the data in Table 1 and fit the data to a straight line, a quadratic, and a logarithmic. o In Part 2 you will download and install Logger Pro and plot the data from Table 1. In Logger Pro you will fit this data to a linear function, a quadratic function, a logarithmic function and compare the fit information with what you found here in the Pivot system. You will also fit the data from Table 1 in Logger Pro to a particular exponential function. - Finally, in Part 3 you will plot the data in Table 2 using only Logger Pro. 5. Which of the four fits is the best fit according to the RMSE value? Is one of the other fits almost just as good or is this one clearly the best? Explain. B I V X X = E @ Vx E OF Score: 0/5 6. If you were told that the data in Table 1 was from measurements of the position of a car as it accelerates down a road but then gradually slows to a stop, would you still think that the best fit model more correctly describes the phenomenon? If yes, why? If not, why not and which model would be better? B IU XX= Score: 0/5v Part 3: Plotting Table 2 in Logger Pro mil} In this part we'll plot the data in Table 2 by using Logger Pro. '_/ (4?); 1. Create a new plot in Logger Pro and change the X column to Time and the Y column to Speed. Enter the data from Table 2 and fit to a function of the form: A*exp(-B*t). You may have to use the Define Function button if this exact function isn't available in Logger Pro. (39' 2. Submit your Logger Pro plot by clicking on the icon that looks like a photo in the answer box below. BIHX1X'EEEEEC'OaFE Score: 0/5 19 3. Is this a good fit to the Table 2 Data? Explain how you know. 3. Is this a good fit to the Table 2 Data? Explain how you know. B I U XX @ VX E FOF E Score: 0/5 4. Can you think of a simpler function that could be an even better fit? (Ask your instructor for a hint.) Try this other function; submit a screenshot of the plot and say a few words about the similarities and differences between the two functions. Which function is actually a better fit? BI U XX @ VX POF Score: 0/5'@ 5. One take away from this activity is that a perfect fit gives a RMSE of zero, but you must be careful. Given any set of data it's _ possible to come up with a crazy function with many parameters (the various coefficients A, B, C, etc.) that will give a zero RMSE. This crazy function probably doesn't match the correct equation that describes the phenomenon being studied. When doing an experiment you usually have some idea of what the correct equation is, therefore doing a curve fit assuming the correct form, or something close, is best practice. Write a paragraph discussing one or two things you learned that might be helpful later in the class or in other classes. Write a second paragraph answering which plotting system, Pivot Interactives or Logger Pro, are you more comfortable using and why? BIUXIX'E EEEEE OOEi.EEI v Score: 0/5 \fv Part 1: Plotting Table 1 / \\'V '6 ) i / i /i\\ Kc, 8. 1. 1. f; -. Plot the data from Table 1 in the introduction and fit to a straight line, a quadratic and a logarithmic. Add the data from Table 1 to the data table below. For the Column Names enter Position and Time. For the Units, enter in and s. For the Variables, enter xand 1*. Notice the ellipsis next to the column names and the row numbers. Click on these to see various things you can do such as adding a column ora formula to populate a column based on values in other columns. Once you've filled in the data table you will plot your data. Click on VerticaiAxisand a little window will pop up. Under Data Column choose Position. Then click on Horizontal Axis and choose Time. Don't worry about uncertainty for either of these axes. To fit the data to a straight line, click on the little cog wheel in the upper right corner of the plot and select Curve Fits. A little window will pop up showing the name of your vertical column, Position. Choose the Linearfunction in the drop- down menu. The curve fit shows a best-fit line through the data and presents an equation of the line. Also displayed is the RMS E, Root Mean Square Error. A perfect fit gives a RMSE of zero. Now, without removing the linear fit from the plot you will fit the data to a quadratic and a logarithmic. To do this, click again on the vertical axis, now labeled Position (m). The little window pops up again. This time click on Add Column and then choose the same Position column as before. (Or you could create new columns, give them different names and copy the data from the original Position column, but this isn't necessary). Now your vertical column label shows the names of the two columns being plotted. Click on the little cog wheel and select Curve Fits. Choose Quadratic for the position data that doesn't yet show a fit model. Repeat the above procedures to add a Logarithmic fit to the data so that you now have three curve fits on a single graph. ' Name Name uh u. u um\". ans.2. 4. To fit the data to a straight line, click on the little cog wheel in the upper right corner of the plot and select Curve Fits. A little window will pop up showing the name of your vertical column, Position. Choose the Linearfunction in the drop- down menu. 5. The curve fit shows a best-fit line through the data and presents an equation of the line. Also displayed is the RMSE, Root Mean Square Error. A perfect fit gives a RMSE of zero. 6. Now, without removing the linear fit from the plot you will fit the data to a quadratic and a logarithmic. To do this, click again on the vertical axis, now labeled Position (m). The little window pops up again. This time click on Add Column and then choose the same Position column as before. (Or you could create new columns, give them different names and copy the data from the original Position column, but this isn't necessary). 7. Now your vertical column label shows the names of the two columns being plotted. Click on the little cog wheel and select Curve Fits. Choose Quadratic for the position data that doesn't yet show a fit model. 8. Repeat the above procedures to add a Logarithmic fit to the data so that you now have three curve fits on a single graph. Name Name units var units var v Graph 1 Title E] 10 Vertical Axis Horizontal Axis Go Back to the Table 1' 2. Which function, linear, quadratic, or logarithmic best fits the data from Table 1? Explain how you know. B I U XX = VX POF Score: 0/5 3. Using the best fit function, calculate the position at a time of 2.0 seconds. B I U X X= VX OF Score: 0/5v Part 2: Logger Pro and Table 1 {.93). In this part we'll look at how to access a copy of Logger Pro and plot the data from Table 1. (5 L): \\_/ 1. Oakton College has a site license for Logger Pro that allows students to download a free copy. The first step is to download the software and install it on your computer. To download and install Logger Pro, go to your course's D2L site and look under Content. You should find a module there titled Getting Logger Pro. In this module is a document containing download links for various operating systems, both current and slightly older. Click on the appropriate link and use your Oakton email address if you are asked to verify your eligibility. If you have any problems downloading and/or installing Logger Pro contact your instructor as soon as possible. The module in D2L also contains a short video showing how to do some basic plotting and curve fitting in Logger Pro. Be sure to watch that video. 9" 2. 1. Open Logger Pro on your computer. 2. As shown in the video, change the X column to be Time with variable t and units, 5. Change the Y column to Position with variable x and units m. 3. Enter the data from Table 1. 4. Click on the curve fit tool and select the linear fit, click Fry Fitand then OK. 5. Add to the plot a quadratic fit and a logarithmic fit. For the logarithmic fit, to get the same functional form as you had (15) 1. Oakton College has a site license for Logger Pro that allows students to download a free copy. The first step is to download the software and install it on your computer. To download and install Logger Pro, go to your course's DZL site and look under Content. You should find a module there titled Getting Logger Pro. In this module is a document containing download links for various operating systems, both current and slightly older. Click on the appropriate link and use your Oakton email address if you are asked to verify your eligibility. If you have any problems downloading and/or installing Logger Pro contact your instructor as soon as possible. The module in D2L also contains a short video showing how to do some basic plotting and curve fitting in Logger Pro. Be sure to watch that video. i- 2. 1. Open Logger Pro on your computer. 2. As shown in the video, change the X column to be Time with variable t and units, 5. Change the Y column to Position with variable x and units in. 3. Enter the data from Table 1. 4. Click on the curve fit tool and select the linear fit, click Try Fitand then OK. 5. Add to the plot a quadratic fit and a logarithmic fit. For the logarithmic fit, to get the same functional form as you had above in Part 1, click on the Define Function button and enterA + B*ln(t). 6. Finally, add an exponential fit of the form, A*(1-exp(-C*t))+B. This is referred to as an inverse exponential fit in Logger Pro. 7. Once you have four fits on your plot you can drag the fit boxes around to clean up the plot. 8. Take a screen shot of your plot for submission in the next section. :9 3. Submit your Logger Pro plot by clicking on the icon that looks like a photo in the answer box below. 6% 3. Submit your Logger Pro plot by clicking on the icon that looks like a photo in the answer box below. BIHXlX'EiEEEwEFE Score: 0/5 39 4. Consider the three fits you did in both the Pivot Interactives system and Logger Pro. Did the fit equations give you the same results or were there differences? Explain. BIHXLX' lll iii III ll ll % [3 EH Score: 0/5 @- 5. Which of the four fits is the best fit according to the RMSE value? Is one of the other ts almost just as good or is this one clearly the best? Explain