1. Pendulum Lab Go to the BPI website, find our class, and download the Pendulum Lab pdf file.

2. Raw Data: Mass Procedure 1 - Raw Data Amplitude (Deg.) Mass (g) Length (m) Period x 20 (s) 201.018 201.018 201.018 201.018 201.018 201.018 201.018 201.018 201.018 Keep Length & Amplitude constant while varying the Mass: 1.Set length to 1.0m. 2.Begin with amplitude of 20 o 3. Use your smallest mass. 4.Record the period for 3 trials: a.Start timing at release of mass. b.Stop after exactly 20 periods c. Record in your data table. 5.Repeat while adding mass 15 30 45 39.76 39.24 38.32 39.96 37.96 39.76 39.04 38.32 30.48

3. Raw Data: Amplitude Procedure 2 - Raw Data Amplitude (Deg.) Mass (g) Length (m) Period x 20 (s) 5451.018 5451.018 5451.018 10451.018 10451.018 10451.018 15451.018 15451.018 15451.018 Keep Length & Mass constant while varying the Amplitude: 1.Set length to 1.0m. 2.Set an amplitude of 5 o 3. Use your largest mass. 4.Record the period for 3 trials: a.Start timing at release of mass. b.Stop after exactly 20 periods c. Record in your data table. 5.Repeat for angles of 10 o, 15 o, and 20 o 38.16 38.88 35.64 38.68 38.32 37.80 38.88 41.40 40.32 You could have saved time by using the data for 20 degrees from Procedure 1.

4. Raw Data: Length Procedure 3 - Raw Data Amplitude (Deg.) Mass (g) Length (m) Period x 20 (s) 20451.0 20451.0 20451.0 20450.8 20450.8 20450.8 20450.6 20450.6 20450.6 20450.4 20450.4 20450.4 20450.2 20450.2 20450.2 Keep Amplitude & Mass constant while varying the Length: 1.Set length to 1.0m. 2.Use an amplitude of 20 o 3. Use your largest mass. 4.Record the period for 3 trials: a.Start timing at release of mass. b.Stop after exactly 20 periods c. Record in your data table. 5.Repeat for lengths of 0.8m, 06m, 0.4m and 0.2m 39.40 40.12 40.68 33.92 33.84 34.00 29.60 29.32 23.56 23.92 24.28 17.08 16.36 17.80

5. Raw Data Change the name of the sheet where you first input your data to “Raw Data” by right-clicking this tab and selecting “Rename” from the popup window.

6. Raw Data Format your data so that it looks like the tables shown. The headings should have units and be bold. All values should be centered; limit all numbers to two decimal places shown.

7. Raw Data Change the names of three other tabs to: Mass, Amplitude and Length. You may need to add one or more tabs by left-clicking here.

8. Null Effect of Mass Copy/paste the Procedure 1 data set onto the Mass sheet and compute the averaged periods by dividing by 20. Try using Excel to do the math…

9. Null Effect of Mass After you’ve found the averaged period, find the average of the three trials for each mass…

10. Null Effect of Mass Next, create a graph of Period vs. Mass as shown here…

11. Null Effect of Amplitude Copy/paste the Procedure 2 data set onto the Amplitude sheet and compute the averaged periods by dividing by 20. Try using Excel to do the math…

12. Null Effect of Amplitude Compute the averaged period and the average of the 3 trials for each angle. Then create a plot of the data, Period vs. Angle

13. Period vs. Length There is a visible curve to the data, so we are on the right track with our deduction. But can we prove the equation definitively???

14. Pendulum Lab – Proving the Deduced Equation: Log Rules: 1) 2) log(mn) = log(m) + log(n) 3) log( m / n ) = log(m) – log(n) 4) log(m n ) = n · log(m)

15. Pendulum Lab – Proving the Deduced Equation: We set out to prove that the period, T, of a pendulum was given by the equation:, and that mass and amplitude have no effect on T. In addition, we also want to determine the constant, C. With the data we have taken, we have the information we need to do this!

16. Pendulum Lab – Proving the Deduced Equation: This equation, is the same thing as saying that, If we plot Log T vs Log L and our deduction is correct, then the slope of the line should be ½!!!

17. Period vs. Length

18. Pendulum Lab – Proving the Deduced Equation: After plotting the Log T vs. Log L and fitting a line to the curve, we now have an experimentally determined equation that can be used to validate our deduced expression. This equation can also be used to help us determine the constant C. Can your team figure out how this might be done???

19. Additional Questions: 1.What were your method(s) for extracting accurate data in the face of difficulties you encountered? 2.Using the data you obtained extrapolate the length of string required for the period of oscillation of the pendulum to equal 2 seconds. Explain your process and show all work. 3.Assuming that the constant C equals 2π, find a best-value for the acceleration due to gravity. Explain your process and show all work.

20. Pendulum Laboratory Report 1.Format: 10% 2.Objectives and Procedures:30% 3.Analysis of results: 30% 4.Error analysis: 10% 5.Questions answered20% Sample Lab Report: http://www.writing.engr.psu.edu/workbooks/labreport2.html (Only difference is that you need to include data plots in the body of your report, not just as an appendix.) Grading Rubric:

21. Pendulum Laboratory Report 3.Write-up a)Typed, 12 pt font, 1.5 spacing b)3-5 pages long, not including appendix of data tables c)Separate report into sections d)Answer #1-3, making sure to cite all sources used a)Describe the purpose of experiment b)Describe the experiment and method c)Describe the results Include data plots and a description of what they tell you – based off objectives d)Describe possible errors that led your results to be different from the theoretical values

22. Pendulum Laboratory Report 3. Write-up (continued) e)How do your graphs and results support or refute the theory of a simple pendulum? Your purpose here is to discuss, in writing, what evidence there is that indicates (or does not indicate) that the theory is correct. Do not do any calculations for this question. Instead, refer to the shapes, features, and types of relations and equations shown on the graph(s). Be sure to discuss each part of the lab.

23. Pendulum Laboratory Report 1.Format: 10% 2.Objectives and Procedures:30% 3.Analysis of results: 30% 4.Error analysis: 10% 5.Questions answered20% Sample Lab Report: http://www.writing.engr.psu.edu/workbooks/labreport2.html (Only difference is that you need to include data plots in the body of your report, not just as an appendix.) Grading Rubric: