CELEN039

Report 1: Simple Harmonic Motion in the Form. of a Pendulum

Foundation Science A

ABSTRACT:

The abstract should be a single paragraph and summarise the overall report. The Abstract should include;

· A statement of the hypothesis being tested in this experiment.

· A brief explanation of how the hypothesis was tested.

· A summary of the conclusion of the report.

You should also refer to “Abstract – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

OBJECTIVES:

State the objective(s) of the experiment, these can be found on the instruction sheet for each experiment.

You should also refer to “Objectives & Introduction – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

INTRODUCTION:

The introduction section should include (in order);

· A brief introduction/history of the pendulum and simple harmonic motion, this should be at most 2 short paragraphs.

· A statement of the hypothesis being tested in the experiment. This should come at the end of your introduction paragraph(s).

· Figure 1 (see below) completed with addition of the relevant forces acting on the pendulum.

· The mathematical derivation of Christiaan Huygens's law, T = 2π g/L, this MUST include reference to Figure 1 and the forces you have added to the diagram. You must show all the steps involved in deriving this equation. Hint: use your textbook to help you.

Figure 1 shows a simple pendulum, with the black dot representing the pendulum bob. You should include Figure 1 in your report and you MUST add the forces acting on the pendulum bob to the diagram and label the forces.

Figure 1. Forces acting on an idealised simple pendulum.

You should also refer to “Objectives & Introduction – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

ASSUMPTIONS:

The assumptions section should take the form. of a bullet point list of the major assumptions of this experiment, do not forget the key assumption that shows that a pendulum bob can undergo simple harmonic motion.

You should also refer to “Objectives & Introduction – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

APPARATUS

The apparatus section should take the form. of a bullet point list, stating all of the equipment/resources that were used to perform. the experiment.

You should also refer to “Apparatus & Procedure – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

PROCEDURE

The procedure should state what was done during the experiment in sufficient detail that another scientist who has not seen the experiment could understand what you have done and could repeat the experiment themselves. The procedure should be written in paragraphs, NOT as a list or bullet points.

A good tip for writing the procedure is to paraphrase the key points of the instruction from the lab worksheet in the past passive voice.

You should also refer to “Apparatus & Procedure – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

RESULTS:

The results section should show the data from the experiment as well as any graphs you have made to analyse this data. This section should also include some sample calculations to show how you worked out various quantities.

The results section should include (in order)

1) A sample calculation showing how you worked out the measured period for one oscillation, Tp_, for measurement 1. This should include a brief explanation of what you are calculating and what equation you are using.

2) A sample calculation showing how you worked out the predicted period, T_p, for measurement 1.

3) Completion of Table 1 with respect to your predicted and measurement results.

4) A suitable graph (Graph 1) to depict the key information in Tables 1 and 3. Use the “Representing Data with Excel” activity on Moodle to help you.

5) Complete Table 2 using the “Uncertainty in Trendlines” Excel file on Moodle. Note if you need help using this resource please review the Representing Data with Excel” activity on the Moodle page.

You should also refer to “Results & Uncertainty Analysis – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

Table 1. Measured and predicted period.

Table 2. Measured and predicted values for the trendline coefficients.

UNCERTAINTY ANALYSIS:

The uncertainty analysis section should contain the tables with your uncertainty values, you can find all the equations you need to use to calculate these values in the “Laboratory Session 1 Uncertainty Guide” on Moodle.

The uncertainty analysis section should include (in order)

1) A sample calculation showing how you worked out the uncertainty for the square root of the measured length, δL1/2, for measurement 1.

2) A sample calculation showing how you worked out the uncertainty for the predicted period, δTp_, for measurement 1.

3) A sample calculation showing how you worked out the standard uncertainty for 1 period, δTm_, for measurement 1.

4) Completion of Table 2 with your respective uncertainty values.

You should also refer to “Results & Uncertainty Analysis – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

Table 3. Uncertainty associated with measured and predicted period.

DISCUSSION:

The discussion section of the report is where you discuss the results of the experiment. It is here you can demonstrate that you understand what the data is telling you by comparing your measured (actual) results with the predicted results.

The discussion is generally split into 3 paragraphs;

· In the first we compare the measured and predicted results (both the table values and the trendline values),

· In the second we consider the correlation coefficients (and what they tell us about the relationship between x and y),

· In the third we look for any patterns in the data and discuss possible reasons why the measured values may differ from the predicted values.

Use the following questions to help you write your 3 discussion (do not just answer the questions: form. your responses into coherent sentences & paragraphs):

Paragraph 1:

· How many of measured results agreed with the predicted results?

· Do the trendline values for the measured data agree with the trendline values from the predicted data (use the values from Table 2, do these values agree within uncertainty or not)?

· Do the trendline values support your hypothesis or not?

· Overall, do the results support your hypothesis or not?

Paragraph 2:

· What does the coefficient of determination, R2 tell you about the how the variables you have plotted on your graph are related?

· What does the product moment correlation coefficient, r, tell you?

· Do the coefficient of determination and product moment correlation coefficient support a straight-line relationship between x and y or not?

Paragraph 3:

· Is there an observable pattern to how the measured and predicted results differ?

· For measured results that differed from your predicted results (outside of the uncertainty range), what are the possible sources of these discrepancies? Hint: consider your assumptions

N.B. It is not enough to say yes or no; your answer must be backed up by referencing data from the results section.

You should also refer to “Discussion – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.

CONCLUSION:

The conclusion section is where you come to a final decision regarding whether or not the experiment supports the hypothesis or not. It should be split into two paragraphs as shown below.

Use the following questions to help you write your conclusion (do not just answer the questions: form. your responses into coherent sentences & paragraphs):

Paragraph 1

· What was the initial hypothesis for the experiment?

· Based on what you have said in the discussion section, does your experiment demonstrate the validity of your hypothesis or not?

Paragraph 2

· Which of the factors from the discussion section is the main source of any measured results differing from predicted results?

· What improved experimental techniques or mathematical models could account for these discrepancies in future investigations?

(N.B. It is not enough to say yes or no; your answer must have been justified in the discussion section and you should refer to what you have said in the discussion section).

You should also refer to “Conclusion – Video Guide” in the “Report Writing” section of Moodle for to help you complete this section.