Physics IA · C · Wave behaviour · topic 13 of 30

Pendulum: when does the small-angle rule break? · IB Physics IA idea: guide, sample graph and step-by-step plan

a classic, but with a twist. good choice :)

Everyone measures g with a pendulum. You're going to catch the textbook formula failing, and find out exactly where.

Difficulty●●○ Medium
KitBasic: string, bob, phone
TimeAbout 10 hours
FitsSL and HL
  • ✓ you like hands-on experiments
  • ✓ you can film with your phone
  • ✓ you want a clear theory to test

The big idea

← this is your RQ hook!

The formula T = 2π√(L/g) only works for small swings. Swing wider and the period creeps up. Your job: measure how much, find where the simple formula stops being good enough, and test the better theory for big swings. Clear prediction, real analysis, an evaluation with actual numbers in it. Examiners like that.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Use a rigid pendulum

A metre rule or rod swinging from one end instead of a bob on a string.

→ New theory (the period depends on how mass is spread out); your graph compares with a different formula, and large amplitudes are easier because nothing goes slack.
Measure damping instead

Keep the amplitude fixed and track how it dies away over time, comparing bob shapes or sizes.

→ Your graph becomes amplitude against time; you fit an exponential decay and compare decay constants. Needs video analysis.
Push to large angles

Go beyond 60°, up to 90° or more, with a rigid rod so it stays taut.

→ The simple formula fails badly, so the large-angle theory is properly tested; you may need more correction terms.
Change how you time

Video analysis frame by frame, or a light gate, instead of a stopwatch.

→ Much smaller timing uncertainty, so you can detect the effect at smaller angles; the evaluation compares methods.
Change the length too

Repeat the amplitude series at two or three lengths.

→ Tests whether the fractional change in period depends on length (theory says it should not): a stronger conclusion.
Change the context

A playground swing, a metronome or a pendulum clock model, scaled down safely.

→ Gives your introduction a real purpose; the physics and the graph stay the same.

Your Physics IA research question: run the check

write it FIRST, then check it

Write your own question first. Then make sure it ticks every box:

  • Names one independent variable and its range (which amplitudes, in degrees, and how many values).
  • Names one dependent variable and how you will measure it (what exactly is "the period"?).
  • Says what stays fixed (length, bob, string, release method).
  • Says what you will compare your result with (the small-angle formula, the large-angle theory, or both).
  • Is narrow enough to answer in about 10 hours, with at least 5 to 7 values and repeats.

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The set-up

One way to set it up. Draw your own version, with your real measurements, for the Method section.

θ₀Lprotractor at the pivot: read θ₀ herebob: keep the same one throughoutphone on a stand,square-onheavy base + clamp

How your Physics IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; why amplitude matters for a pendulum clock, a swing or a seismometer; what you expect and why.
Background physics~450
The small-angle period formula and the assumption behind it; the large-amplitude correction you will test (cite where it comes from); what your graph should look like if theory holds.
Variablestable
Independent, dependent and controlled variables, each with how you set, measure or keep it constant, and why it matters.
Method~400
Apparatus with resolutions; how you release at a known angle; how you time (how many oscillations per reading and why); repeats; enough detail that someone could copy it.
Safety, ethics, environment~60
Short and specific to your set-up (clamp stand stability, swinging mass).
Raw datatable
One clear table: amplitude, each timed reading, units and uncertainties in the headers.
Processing~250
How you get the period and its uncertainty from repeated timings; one worked example of each calculation type.
Graphs and analysis~350
The graph you choose, why, error bars, line of best fit and what its gradient and intercept mean physically.
Conclusion~450
Answer the question with numbers: the amplitude where the simple formula is off by more than your uncertainty; how your data compares with the large-angle theory.
Evaluation~650, the biggest part!
Strengths, weaknesses ranked by their effect on your result, and realistic improvements linked to each weakness.
Referencesnot counted
Every source you used for theory or method.

What your Physics IA graph could look like

error bars on EVERY point ✓

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only

010203040506070801.781.801.821.841.861.881.901.921.941.961.982.00Release amplitude θ₀ / ° (± 1°)Period T / slarge-angle theorysmall-angle formulayour data, with error barsdata leaves the dashed line here:where is the gap bigger than your error bars?ILLUSTRATIVE · MADE-UP DATA
  • Axis labels name the quantity and its unit, with the uncertainty of the variable you set.
  • Error bars on every point. Here the timing uncertainty is bigger than the angle uncertainty, so the vertical bars are the long ones.
  • Both theories drawn so the reader can see which one your data follows.
  • The scale starts near your data, not at zero, so the small effect is visible. Say so in the text.
  • Another graph to consider: plot T against θ₀² (θ₀ in radians). If the first correction term dominates, it is close to a straight line, and its gradient and intercept can be compared with theory.

Which uncertainty matters most?

rank them: don't just list them

Rank by the effect on your result (here, the small extra period), not on the raw readings. A quick chart like this, with your numbers, makes it obvious, and often shows the fix: here, better timing.

Timing 10 swings (±0.10 s)33%Amplitude decay during timing13%Release angle θ₀ (±1°)7%String length L (±1 mm)0.1%biggest effect: discuss this first!% uncertainty in your result: the extra period ΔT at θ₀ = 30°ILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

don't skip the trial run! it saves you weeks

Tick steps off as you go. We'll remember on this device.

0 of 10 done

  1. Read and predictFind the small-angle period formula and a source for the large-amplitude correction. Before touching apparatus, write down what you predict will happen to the period as amplitude grows, and roughly where you expect a 1% difference.
  2. Trial run (1 lesson)Try a few amplitudes. Is your release repeatable? Does the swing stay in one plane? Does the amplitude die away during the timed oscillations? Fix the problems now.
  3. Decide range, repeats and timingChoose at least 5 to 7 amplitudes across a wide range, decide how many oscillations to time per reading, and how many repeats. Write down why for each choice; this becomes your method justification.
  4. Collect the dataRecord raw readings straight into your table with units and the instrument's resolution. Note anything odd as it happens (it becomes evaluation evidence).
  5. ProcessTurn timings into periods with uncertainties. Decide how you will handle the uncertainty of the amplitude itself, not just the time.
  6. Graph and fitChoose a graph that lets you test the theory with a straight line if you can, and decide what the gradient and intercept should be if the theory holds. Add error bars. Check whether the line passes through them.
  7. Compare with theoryWhere does your data separate from the simple formula? Does it follow the large-angle theory? By how much, compared with your uncertainties?
  8. EvaluateWhich uncertainty or systematic error mattered most to your answer? Rank them. Make every improvement specific to a weakness you found.
  9. Write, then cutWrite in the order of the layout above. Keep within 3,000 words: tables, graphs, equations and references are not counted, so let them carry detail.
  10. Check before your teacher's draftRun the checklist below, then get your RQ or draft checked. Your teacher reads one draft only, so make it count.

Physics you'll need

Traps to avoid in this Physics IA

  • Timing a single swing: human reaction time swamps the effect you are looking for.
  • Amplitude that decays during the timed oscillations, so the "amplitude" you recorded is not the one you measured.
  • Too narrow a range: below about 20° every point agrees with the simple formula and there is nothing to analyse.
  • A string that stretches or a clamp that wobbles: a hidden change in length.
  • Uncertainty only on time, none on angle.
  • An evaluation that lists "human error" without saying which measurement and how big.

More Physics IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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