Physics · Oscillations
Find g with a simple pendulum and a phone
Time pendulums of different lengths and get the acceleration due to gravity from a straight-line graph.
- DifficultyEasy
- Estimated time1–3 hours
- BudgetUnder ₹250
- ClassClass 9–12
- TeamSolo or up to 2
- You needHousehold materials
Prerequisites: Period and frequency
Original · by TechnifyedExperimentInvestigationBeginner friendlyLow costResearch orientedWell documented
Overview
The period of a pendulum depends only on its length and on g. Time twenty swings for five lengths, plot T² against L, and the slope gives g.
Why build this?
It is the classic board-practical experiment, and doing it carefully shows how a graph beats a single calculation.
What you will learn
- Why T² is proportional to L
- How timing many swings reduces error
- How to get a constant from the slope of a graph
Skills you will use
Materials and tools
- Thread about 1.5 m
- Small heavy bob (a nut or stone)
- Fixed support such as a door frame hook
- Metre scale
- Stopwatch or phone
Tools and software
Step-by-step roadmap
Start
You will finish with: a table, a straight-line graph and a value of g with percentage error.
- 1
Prerequisites
Know this first: period and frequency. Then collect the 5 items in the materials list.
- 2
Learn
- Why T² is proportional to L
- How timing many swings reduces error
- How to get a constant from the slope of a graph
- 3
Plan
Write your question, your hypothesis and the one thing you will change. Draw the table you will fill in before you start.
- 4
Build
- Hang the bob so its length from the support to the centre of the bob is 30 cm.
- Pull it aside by a small angle (under 10°) and release without pushing.
- Time 20 complete swings and divide by 20 to get T.
- Repeat for lengths of 50, 70, 90 and 110 cm.
- Plot T² (vertical) against L (horizontal) and draw the best straight line.
- Calculate g = 4π² ÷ slope.
- 5
Test
A careful run gives g between 9.6 and 10.0 m/s².
- 6
Document
Record every reading with its unit, photograph the setup and draw a graph of the result. Report structure
- 7
Present
Explain the question, the method and the graph in two minutes; keep the setup ready to demonstrate. Presentation structure · Viva questions
- 8
Publish
Share the report and photos with your class, a science fair or your school magazine.
Expected outcome
A table, a straight-line graph and a value of g with percentage error.
Other versions of this project
Beginner version
Use one length and the formula directly.
Advanced version
Use a phone accelerometer app to record the swing and extract the period from the data.
Research version
Measure how the period changes at large amplitudes (20° to 60°) and compare with the first correction term to the simple formula.
Make this project better
- BasicUse one length and the formula directly.
- This projectFind g with a simple pendulum and a phone
- AdvancedUse a phone accelerometer app to record the swing and extract the period from the data.
- ResearchMeasure how the period changes at large amplitudes (20° to 60°) and compare with the first correction term to the simple formula.
Ways to do this project
Text marked "You write this" is a prompt for your own work; everything else is specific to this project.
- Problem
- You write thisWrite your question as: How does [what you change] affect [what you measure]?
- Hypothesis
- You write thisWrite it as: If [I change this], then [this will happen], because [reason].
- Variables
- You write thisName the one thing you change (independent), the thing you measure (dependent) and what you keep the same (controlled).
Materials and procedure are in Materials and the Roadmap.
Observation table
You write thisDraw a table with one column for what you change, one for each repeat reading and one for the average.
- Graph
- You write thisPlot what you changed along the bottom and what you measured up the side; use a bar chart for categories and a line graph for numbers.
- Results
- You write thisState what the graph shows in one or two sentences, with numbers.
- Conclusion
- You write thisSay whether the result supports your hypothesis and why you think so.
Display board
- Title and your name
- Question
- Hypothesis
- Materials
- Procedure (with photos)
- Data table and graph
- Conclusion
- What you would do next
Questions judges ask
- Why keep the angle small?
- Why time 20 swings?
- Does the mass of the bob matter?
- What would you change if you did this again?
- What was your biggest source of error, and how did you reduce it?
- Where is this idea used in real life?
- Research question
- You write thisOne question you can answer with data, narrow enough to finish in the time you have.
- Hypothesis
- You write thisWhat you expect to find, and why.
- Variables
- You write thisWhat you change or compare, what you measure, and what you hold constant.
- Methodology
- Measure how the period changes at large amplitudes (20° to 60°) and compare with the first correction term to the simple formula.
- Data collection
- You write thisSay what you will record, how many times, and how you will keep the records safe.
- Analysis
- You write thisChoose the table, chart or test that answers the question; report averages with their spread.
- Limitations
- You write thisList what could have affected the result: small sample, instrument limits, things you could not control.
Literature review
Find five to eight sources (your textbook, review articles, reports) and note what each says about your question. Group them by idea, not one after another, and end with what is still not known.
References
List every source you used in one style throughout (author, year, title, where it was published, link and the date you opened it).
Working as a team
Solo or up to 2. Suggested roles:
Report and presentation
Report structure
- Title and question
- Background: the science behind it
- Hypothesis
- Materials
- Method (steps, with a diagram or photo)
- Observations (table)
- Results (graph and calculation)
- Sources of error
- Conclusion
- What you would do next
- References
Presentation structure
- The question
- Why it matters
- The idea behind it
- Setup (photo)
- Method in three steps
- Results (one clear graph)
- What the result means
- Errors and limits
- Conclusion and next step
Viva questions
Try answering before you open each one.
Why keep the angle small?
The formula T = 2π√(L/g) holds only for small swings.
Why time 20 swings?
A reaction-time error of 0.2 s is spread over 20 swings.
Does the mass of the bob matter?
No, the period is independent of mass.
Where is the length measured to?
The centre of mass of the bob.
Resources
Source and attribution
Original
Written by Technifyed. Free to use for your own school or college project; write the report in your own words. Added 1 Oct 2026.
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