Pendulums: An Introduction to the Scientific Method

Unlike many labs you may have had in other science courses, experiments in this course will not come with a detailed step-by-step manual. Instead, you will make observations and explore phenomena, design your own experiments, and make choices about how to revise and improve your work as you go along. It will take a bit of practice, so don’t get discouraged!

Today you will be working with pendulums. It’s OK if you don’t know anything about pendulums or if you haven’t seen anything about them in the lecture! Experimental physics often looks at new phenomena and you don’t need to know any underlying theory in order to do an experiment.


By the end of this lab, you will be able to…

  • Collect data and revise an experimental procedure iteratively and reflectively,
  • Evaluate the process and outcomes of an experiment quantitatively and qualitatively,
  • Extend the scope of an investigation whether or not results come out as expected,
  • Communicate the process and outcomes of an experiment, and
  • Conduct an experiment collaboratively and ethically.

E-CLASS survey

Before beginning the lab, we are asking all students to complete an assessment survey which helps the Department of Physics Instructional Laboratories staff understand how student attitudes about experimental physics change as a result of this course. Today's survey is a pre-survey to understand your attitudes coming in to this class. There will be a second post-survey at the end of the course that will look for changes.

The survey will not affect your grade. Instructors and TAs will never see your individual responses. Identifying information is collected only so the survey administrators can connect the pre- and post-surveys.


The structure of the lab

One of the main purposes of the physics labs in this course is to learn how scientists study the world around them. With a focus on the scientific process of asking questions and doing an experiment, students can learn how to think like a scientist.

Each lab has a similar structure.

  • Students will work in groups of 3.
    • All students are expected to work with the equipment and get experience handling apparatus and taking data.
  • Each group will keep an electronic lab notebook.
    • The group should work on the notebook throughout the period, and the TA may ask to look at as they walk around checking on groups.
    • All students are expected to contribute ideas to the notebook, and the person doing the recording should rotate through group members.
    • It is not formal, but it should be neat and organized.
    • It is a record of work done, and it is a place to make sketches, do quick calculations, or to write thoughts or questions.
    • Do not delete or erase. Instead, carefully indicate sections that you want to change (e.g. by making them a different color and adding a note); the notebook is a record of everything, including mistakes.)
  • The group notebook is also the report for the group which will be graded. In addition to text, feel free to include photos or drawings in the report.
    • Did you build something? Make a sketch.
    • Did you observe something? Record what you see.
    • Did you ask a question? Write it down.
    • Did you collect data? Make a table.
    • Did you calculate quantities? Show your work.
    • Did you make a plot? Put a copy in the report.
  • Groups also have access to a whiteboard to share thoughts and ideas with each other and with other groups.

The scientific method

Fo this lab, we will consider the process of scientific investigation as being made up of the following five stages:

  • Observation
  • Hypothesis and Prediction
  • Experimentation and Analysis
  • Communication
  • Revision

Not every lab period will include every step. Some labs will focus on one part of the process only, while others will look at the process as a whole.

In this week's lab, the TA will lead you explicitly through each of these steps.

The pendulum

A pendulum is any mass which – when pulled away from its starting position – will oscillate back and forth. Think of a grandfather clock or a metronome. Don't worry if you haven't yet encountered pendulums in lecture; you do not need to know any theory in order to test the model.

Today you will build a simple pendulum which has most of the mass, $m$, concentrated in a single bob at the bottom of a string of length $L$. When you pull the mass back so that the string forms an angle $\theta$ – or equivalently so that it moves out to an amplitude $A$ away from the vertical – and release it, the mass will swing back and forth, returning approximately to where it started after each cycle. The time it takes to complete a single cycle – that is, to go from one extreme to the other and back to where it started – is called the period, $T$. Equivalently, we can also measure the number of cycles that happen in a set length of time; this is the frequency of the pendulum, $f$, and it's equal to the reciprocal of the period:  $f=1/T$ .

Independent, dependent and control variables

An independent variable is a variable which you have control over. It is the variable which you can change from trial to trial.

A dependent variable is a variable which you measure. It is the variable which changes in response to your changes in the dependent variable.

A control variable is a variable which you keep fixed during an experiment. You want to make sure that all variables which are not independent or dependent are controlled, or else it may become difficult to tell what changes you are making are causing the outcome you measure.

Consider the following example:

A student wishes to measure the effectiveness of the brakes on a particular model of car. They have access to a professional driver and a closed track, as well as typical measurement tools like a stopwatch, tape measure, etc. What experiment could the student design? What would be good choices for the independent variable(s)? The dependent variable(s)? The control variable(s)?


For this lab, you will work in groups of three. The TA will introduce the equipment available and guide you through the lab.

Your TA will provide more details on each step, but you can consult the outline below as you progress. Remember to write down everything you see and do in your group lab notebook.

  • Use the digital group lab report to communicate the process and results from your experiment.
  • Make sketches, do calculations, take notes, and record observations.
  • Your TA may ask to see your notebook during lab, and will read over it afterwards to assign a grade to the group.

Remember also that you will need to share your experiment and its results with the class at the end of the period. It may be helpful to use the whiteboards to make diagrams, notes, tables, or plots of information you want to communicate to others as you go.


You will receive a single grade for each experiment out of a maximum of 10 points. This grade is based on an in-lab participation score (4 points, awarded individually) and a group lab report submitted electronically to the TA at the end of the lab period (6 points, awarded as a group).

Grading is based on the following rubric:

Acceptable (4) Needs Improvement (2) Not Acceptable (0)
Participation (Individual) Participates in a meaningful way in all aspects of the lab including group discussion, class discussion, data taking, record keeping, analysis, and clean-up. Is distracted or reluctant to participate, or is missing for part of the lab period. Allows partners to do most of the work. Arrives late or leaves early. Takes a superficial data set with no attempt to analyze data and improve measurements in order to leave the lab early. Is disruptive or otherwise disrespectful to the group or the class.
Acceptable (2) Needs Improvement (1) Not Acceptable (0)
Report: Experimental Procedure (Group) Experimental procedure adequately described, including diagrams as needed. Reasons given for decisions made regarding procedure. Sources of uncertainty are clearly described. Decisions regarding how uncertainties will be estimated are presented clearly. Some elements of the experimental procedure are omitted or unclear. No justification given for choices made during the experiment. Important sources of uncertainty were missed. No reasons presented for how uncertainties were estimated. It is unclear how the experiment was performed. No uncertainties considered.
Report: Data and analysis (Group) Data are clearly presented in tables and graphs. All tables and graphs are appropriately labeled and include units. Uncertainties in data are estimated and justified, and their impact on the results is discussed. Some data not recorded. Tables or graphs inadequately or incorrectly labeled. No units assigned to measured values. Uncertainties estimated but not justified or discussed. No data present in report. Data presentation is confusing and does not relate to description of experimental procedure. No treatment of experimental uncertainties.
Report: Conclusions (Group) Conclusions are clearly supported by the data. Comparison of data to models or predictions include assessment of uncertainties. Conclusions are overstated based on the data. Conclusions are contradicted by the data.

Your TA will grade your group's report and return it with a grade before your next lab period.

Outline of the lab

Make preliminary observations

Consider: What happens as you change one variable and keep the others the same? In what ways can you measure your results? Can you make these measurements more accurate?

Construct a well-defined experimental question

Consider: What is your independent variable? Your dependent variable? Your control variables? What is your hypothesis for this experiment and what specific prediction does it make?

Design your experimental apparatus

Consider: What materials do you require? How will measurements be taken? By what methods are control variables being considered? What tools can be used to decrease the experimental error in the lab setup?

Perform the experiment

Consider: Do you trust your measurements? What uncertainties are present in the data and how can you quantify them? If measurements are repeated, do you get similar results?

Analyze the data

Consider: How can you represent your results? Does any relationship exist between the variables being looked at? Are your data consistent with your prediction? Inconsistent? Inconclusive?

Communicate your results

Consider: What do you want others to know about your experiment? How can you present your methods and results succinctly and clearly? Can you anticipate questions others might have? Can you think of improvements you’d make if you had more time?


At the end of the lab, you will need to record your final conclusions (about 1 or 2 paragraphs) in your lab report summing up the important results and take-away points from your experiment. Remember that you should only draw conclusions which are supported by the data, so be ready to back up any statements you make!

When you're finished, save your file as a PDF and upload it to Canvas. (Only one student needs to submit the report, but make sure everyone's name is on it!) If you make a mistake, you can re-submit, but work done after the end of the lab period will not be accepted.

Remember to log out of all your accounts after you submit!