Pendulum Lab Data Analysis Objective: Review Pendulum Lab Data Analysis, Error/Uncertainty Review Pendulum Lab Grades, Marks, and Lessons Learned

Pendulum Lab Objectives To support the theory that the relationship between the period of oscillation, T, and the length, l, of a simple pendulum (see Figure 1) is of the form . To deduce the value of the constant, C, in the equation for the period of oscillation of a simple pendulum. In effect, we will prove that the constant is equal to 2p. To observe the null effect of the mass, m, on the period of oscillation. To observe the effect of varying the amplitude on the period (for angles less than 22o, the amplitude effect is null). Reword these as hypotheses…

(we’ll get to that later) Model Data Tables: Data Tables should reflect appropriate number of significant figures – these tables do not (we’ll get to that later)

Equipment Subsection

Data Subsection

Data Subsection

Data Subsection

Data Analysis Subsection

Data Analysis Subsection The R2 term is a measure of how well the trendline approximates the real data points. Ranges from 0 to 1; 0 is a poor prediction, 1 is a perfect prediction (not likely to ever get this close). Close to 1 is good; Close to 0 is bad An R2 of 0.8 indicates that 80% of the change in one variable is explained by a change in the other

– Obj 1 Prediction based on derivation: y = m * x

C = 2p – Obj 2 If Then

C = 2p – Obj 2

T not affected by m – Obj 3

Why is an R2 of 0.22 not significant in this case? T not affected by m – Obj 3 The R2 term is a measure of how well the trendline approximates the real data points. Ranges from 0 to 1 – 0 is a poor prediction, 1 is a perfect prediction (never likely) An R2 of 0.8 indicates that 80% of the change in one variable is explained by a change in the other Why is an R2 of 0.22 not significant in this case?

T not affected by A – Obj 4

Uncertainty Mass – instrument Length – instrument + estimation Amplitude – estimation Period – average deviation of tests Constant – measured (average deviation) and calculated (relative error in calculation)

Error With most school experiments, the accepted value is known. Error calculations are based on comparison between measured values and accepted values. Cmeasured = 6.0 + 0.2 Ctheory = 6.2831… What’s the error in the measured value?

Sum or difference What is the error if you add or subtract numbers? The absolute error is the sum of the absolute errors.

Product or quotient What is error if you multiply or divide? The relative error is the sum of the relative errors.

Multiply by constant What if you multiply a variable x by a constant B? The error is the constant times the absolute error.

Powers and exponents What if you square or cube a number? The relative error is the exponent times the relative error.

Lab Questions Should be answered in the body of the report, not as stand-alone bullets or in unrelated paragraphs/sections. What unexpected or expected difficulties did you encounter in the procedure, and what were your method(s) for extracting accurate data in the face of those difficulties? What length of string is required for the period of oscillation of the pendulum to equal 1 second. What usefulness does this information provide? Explain your solution and show all work. Using your raw data for period and length, and using your value for the constant C, find a best-value for the acceleration due to gravity. Explain your process and show all work.

Lab Report – Discussion/Conclusion Introduction Procedure Results Discussion Lab Report – Discussion/Conclusion The meat of the lab report: Give a brief recap of your question and hypothesis. Was your hypothesis correct? What happened and why? Were there any difficulties with the experiment? Is there any reason to disbelieve your results? How could you improve the experiment? Do these results suggest any follow-up experiments? Answer all lab questions. Be Specific and Quantitative – back it up with numbers, or else you probably shouldn’t say it

With your partner… Add notes to your “lessons from mistakes” sheet in your notebook. What new insights into technical reports have you gotten from these lectures? What will you never again do in a lab report that you did in your pendulum lab report? What will you always do in a lab report that you hadn’t thought of before? Who will be revising which part, and by when will the report be: Complete Proofread by each group member Submitted to another group for proofreading (schedule this now with another group)