Physics IA · C · Wave behaviour · topic 14 of 30
Mass on a spring: does the spring's own mass matter? · IB Physics IA idea: guide, sample graph and step-by-step plan
a gentle start, but it can go deepThe textbook formula treats the spring as having no mass. Yours has some. You're going to find out how much that matters.
- ✓ you like hands-on experiments
- ✓ you can film with your phone
- ✓ you want a clear theory to test
The big idea
← the intercept is your RQ hook!For a mass m on an ideal spring, T = 2π√(m/k), so a graph of T² against m is a straight line through the origin. A real spring also moves, and about a third of its mass joins in, so T² = 4π²(m + mₛ/3)/k. The line should cut the T² axis above zero. Test the ideal model, spot where it fails and find mₛ from the intercept. You can also check k independently, by stretching the spring statically.
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 →
Measure k from the period and by hanging masses and measuring extension.
→ Two independent values of k to compare; the evaluation asks why they might differ.Use the intercept of T² against m to estimate mₛ and compare with weighing the spring.
→ Turns a systematic error into a result; the graph's intercept becomes a quantity you can check.Use two or three springs with different stiffness or length.
→ k changes; the analysis tests how k and mₛ depend on the spring.Compare springs in series and in parallel.
→ Tests how k combines; the graph has several lines with different gradients.Track how the amplitude dies away for different masses or surfaces.
→ Graph becomes amplitude against time; fit an exponential decay and compare decay constants. Needs video analysis.A car suspension, a trampoline or a bathroom scale.
→ Gives the introduction a purpose; the physics and graph stay the same.Your Physics IA research question: run the check
write it FIRST, then check itWrite your own question first. Then make sure it ticks every box:
- Names one independent variable and its range (hanging mass, how many values, from what to what).
- Names one dependent variable and how it is measured (period from how many oscillations, by what method).
- Says what stays fixed (spring, amplitude, release method).
- Says what you compare with (the ideal formula, the corrected formula, or a static value of k).
- Is narrow enough for about 10 hours, with at least 6 masses and repeats.
The set-up
One way to arrange it. Draw yours with the real spring and measurements for the Method section.
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.
Your question; where spring oscillations matter (suspension, scales); what you expect and why.
Hooke's law and the period of a mass-spring system; why a spring with mass changes the result; how T² against m should look.
Independent, dependent and controlled variables, each with how you set, measure or hold it, and why it matters.
Apparatus with resolutions; how the spring is hung and the amplitude set; how many oscillations you time and why; the mass of the spring; repeats.
Short: stability of the stand, masses falling, eye protection.
One clear table: mass, each timed reading, units and uncertainties in the headers.
Time for N oscillations to period and its uncertainty, then T²; one worked example per type.
T² against m with error bars, best and worst fit lines; what the gradient and intercept mean physically.
Answer with numbers: k from the gradient, whether the intercept matches a spring-mass correction, and how the model holds.
Weaknesses ranked by their effect on your result, each linked to a realistic improvement.
Every source for theory and method.
What your Physics IA graph could look like
look at the intercept ✓Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only
- Plotting T² against m turns the theory into a straight line.
- Error bars on every point. Squaring T doubles its fractional uncertainty, so say how you propagated it.
- Both model lines are drawn, so the reader can see which one the data follows.
- Check the intercept as carefully as the gradient: it carries the spring's own mass.
- Another graph to consider: T against √m, which should be straight for the ideal spring; compare which graph exposes the correction better.
Which uncertainty matters most?
Rank by the effect on your result, here k from one point. The biggest term is often the model, not the instrument.
Your game plan
Tick steps off as you go. We'll remember on this device.
0 of 11 done
- Read and predictFind the period of a mass-spring system and the correction for the spring's mass. Predict how T² varies with m, and where the line crosses the T² axis.
- Trial run (1 lesson)Hang a mass and time 10 oscillations. Does it bounce straight? Does the amplitude die away over the timed oscillations? Fix the problems now.
- Weigh the springMeasure the spring's mass on a balance. You need it to test the correction.
- Decide range, repeats and timingChoose at least 6 masses across a wide range, how many oscillations to time, and how many repeats. Write down why.
- Collect the dataRecord raw readings straight into your table with units and resolution. Note anything odd.
- ProcessTurn timings into periods with uncertainties and then T². Decide how you handle the uncertainty of the mass.
- Graph and fitPlot T² against m with error bars. Fit best and worst lines and read off the gradient and the intercept.
- Compare with theoryWhat does the gradient give for k? Does the intercept match a third of the spring's mass? By how much, compared with your uncertainties?
- EvaluateRank the weaknesses by effect on your result. Make each improvement specific to a weakness you found.
- Write, then cutWrite in the order of the layout and stay within 3,000 words. Tables, graphs and references do not count.
- Check before your teacher's draftRun through the checklist below, then get your RQ or draft checked. Your teacher reads one draft only.
Physics you'll need
Traps to avoid in this Physics IA
- Ignoring the spring's own mass and then blaming the intercept on "error".
- Too narrow a mass range, so the intercept is poorly determined.
- Timing a single oscillation: reaction time swamps the effect.
- Amplitude so large the spring behaves non-linearly, or so large the mass bounces off the hanger.
- A swinging or twisting mass, not a clean vertical oscillation.
- Measuring the length of the spring but never its mass.
- An evaluation that lists "human error" without saying which measurement and how big.
More Physics IA ideas like this
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- Refraction: how closely does light obey Snell's law?●○○
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.