17 of 17 ideas
C.1 Simple harmonic motion: 17 ideas
Testing T squared against length for a simple pendulum
Research question. How does the length L of a simple pendulum, varied from 0.20 m to 1.00 m in steps of 0.10 m, affect its period T, and does the gradient of T² against L match 4π²/g?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Common: on 3 sites
My take. Very safe but also very common, so it will not impress by itself. Make it yours by measuring g for a specific reason, such as comparing it with a phone accelerometer value or checking it at your own location, and be strict about the intercept.
Method, physics and where marks are lost+
- Independent variable
- String length from pivot to centre of the bob, 0.20 to 1.00 m, 9 values, each set up three times.
- What you measure
- Time for 20 oscillations with a stopwatch or a light gate, divided by 20 to give T. Then T² is calculated and g is found from the gradient.
- Controlled variables
- Release angle kept under 10° using a printed protractor sheet clamped behind the string. Same steel bob throughout. Same thin inextensible thread. Pivot held in a clamp with a slit so the length does not creep.
- Physics and graph
- T = 2π√(L/g) for small angles. Plot T² (y) against L (x). The gradient is 4π²/g, so g = 4π²/gradient. A non-zero intercept points to a length measurement error, for example the bob radius.
- SL and HL
- SL students can plot the line, extract g and compare with 9.81 m/s². To reach the top band, add a proper uncertainty analysis with max and min gradients and explain any intercept. HL students can go further by fitting a power law T = kLⁿ and testing whether n = 0.5 within uncertainty.
- Where marks are lost
- Research design: no justification for the range of L or for keeping the angle small. Data analysis: uncertainty in T taken from the stopwatch resolution rather than from spread and reaction time. Conclusion: g quoted without a percentage difference from the accepted value. Evaluation: this topic is heavily used, so weak, generic evaluation stands out.
- Data
- Needs only a stand, thread, bob, metre rule and stopwatch, and the main uncertainty is timing reaction time and measuring L to the bob centre.
Where the small-angle pendulum formula stops working
Research question. How does the measured period of a 1.00 m pendulum change as the release angle increases from 5° to 80° in steps of 15° or so, and at what angle does it differ from 2π√(L/g) by more than the uncertainty?
- C.1 Simple harmonic motion
- SL and HL
- Needs care
- Common: on 3 sites
My take. Much better than the plain length and period task because it asks where a model breaks, which is what examiners like. Choose it if you are comfortable with a little series expansion.
Method, physics and where marks are lost+
- Independent variable
- Release angle, 5°, 10°, 20°, 30°, 45°, 60°, 70°, 80°, each with three repeats.
- What you measure
- Period from video analysis at 240 fps or a light gate over 10 swings. Calculated quantity is the percentage difference between the measured T and the small-angle T₀.
- Controlled variables
- Length fixed and measured once with a rule and again after the experiment. Same bob and thread. Room draughts limited by working away from doors. Number of swings timed kept identical so amplitude decay is similar.
- Physics and graph
- T₀ = 2π√(L/g), while the exact period is T ≈ T₀(1 + θ₀²/16 + 11θ₀⁴/3072 + …) with θ₀ in radians. Plot T/T₀ (y) against θ₀² (x). The gradient should be near 1/16 for modest angles.
- SL and HL
- SL students can plot T against angle and state where the deviation exceeds error bars. Top band work compares against the series correction and discusses damping. HL students can compare with the elliptic integral result numerically.
- Where marks are lost
- Research design: angle measured by eye, giving large uncertainty on small angles. Data analysis: uncertainty in θ ignored when deciding where deviation starts. Conclusion: claiming a single failure angle without a stated threshold. Evaluation: amplitude decay during timing not discussed.
- Data
- A phone camera in slow motion or a light gate is needed, and the biggest uncertainty is reading the release angle and amplitude loss over several swings.
Effective spring mass from oscillation period against load
Research question. How does the period of a vertical spring oscillator depend on the hanging mass from 50 g to 300 g, and what fraction of the spring's own mass is effective?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Common: on 2 sites
My take. Basic but very safe, and the intercept analysis lifts it above the ordinary version. Twist: compare two springs of different mass to see the ms/3 term change.
Method, physics and where marks are lost+
- Independent variable
- Hanging mass from 50 g to 300 g in 50 g steps, six values, with the period timed over 20 oscillations and repeated three times.
- What you measure
- Period found by timing 20 oscillations with a stopwatch or by a motion sensor or a phone video. Calculate T² and compare with the load.
- Controlled variables
- Same spring, with the amplitude fixed at about 2 cm and checked by a ruler. Same starting point and release without sideways motion. Same clamp height. Masses measured on a balance and the spring mass measured separately.
- Physics and graph
- T² = 4π²(m + ms/3)/k for a spring of mass ms. Plot T² against m. The gradient is 4π²/k and the negative intercept on the m axis is ms/3, which can be checked against the balance.
- SL and HL
- SL can find k and show T² is linear in m. Top marks come from getting the intercept and testing the one third factor against the measured spring mass, and checking k against a static extension test. HL can derive the one third factor by integrating the kinetic energy of the spring.
- Where marks are lost
- Data analysis: plotting T against m and not linearising, or forcing the line through the origin. Evaluation: timing errors on few oscillations and ignoring damping and non-linear extension at low load. Research design: no independent check of k.
- Data
- Needs a spring, slotted masses, clamp stand, stopwatch or phone; the main uncertainty is reaction time, reduced by timing many swings.
Card area and amplitude decay of a spring mass oscillator
Research question. How does the area of a card (10 to 100 cm2, 6 values) fixed to a mass on a spring affect the amplitude remaining after 20 oscillations?
- C.1 Simple harmonic motion
- SL and HL
- Needs care
- Rarely listed
My take. Solid and doable. Equalising the mass across cards is the detail that makes it credible, and adding a bare-mass run gives a proper baseline.
Method, physics and where marks are lost+
- Independent variable
- Card area from 10 to 100 cm2, cut from the same card into 6 sizes and measured with a ruler. Three trials per size.
- What you measure
- Amplitude after 20 oscillations from a phone slow video against a ruler, or a motion sensor; calculate the ratio A20/A0 and the damping constant from ln(A20/A0).
- Controlled variables
- Starting amplitude fixed at 5.0 cm; total oscillating mass kept constant by adding plasticine to smaller cards; same spring; card kept horizontal and flat facing the motion.
- Physics and graph
- Air drag is roughly proportional to area and v squared, giving amplitude decay. For light damping A = A0 exp(-bt/2m); plot ln(A20/A0) against area and test proportionality.
- SL and HL
- SL students plot ratio against area and describe the trend. Top band work justifies whether drag is linear or quadratic, and compares damping constants using ln of amplitude.
- Where marks are lost
- Research design: the card mass changes with area and hides the effect. Data analysis: reading amplitude off a video with large parallax. Evaluation: the spring's own damping and card tilt are not discussed.
- Data
- Needs a spring, masses and phone video; the main uncertainty is amplitude reading, so use a ruler in the frame and a tripod.
Damping of a pendulum swinging in liquids of different viscosity
Research question. How does the amplitude decay constant of a pendulum bob in water change as glycerol is added, from 0% to 50% by volume in 10% steps?
- C.1 Simple harmonic motion
- SL and HL
- Needs care
- Rarely listed
My take. Much better than a simple fluid comparison, because the glycerol mixture gives a numerical IV. Use a small dense bob and a slow swing so the drag stays roughly linear.
Method, physics and where marks are lost+
- Independent variable
- Glycerol concentration in the water, 0 to 50% by volume in 6 values, prepared in a tall container; 3 runs at each concentration.
- What you measure
- Amplitude read from a video at 60 fps or more, using Tracker software, at successive peaks. Calculate the decay constant from the gradient of ln(amplitude) against time. Also record the period.
- Controlled variables
- Same bob, string and pivot point; same starting amplitude of about 5 degrees; liquid temperature checked with a thermometer, as viscosity is temperature dependent; bob fully submerged at the same depth with the container wide enough to avoid wall effects.
- Physics and graph
- Damped oscillation has amplitude A = A0 e-γt. Plot ln A against t; the gradient is -γ. For small speeds the drag is proportional to velocity, so γ should rise linearly with viscosity; plot γ against viscosity from tables.
- SL and HL
- SL: decay constants and a graph of γ against concentration. Top band or HL: compare with the Stokes' drag prediction, discuss the Reynolds number, and account for the added mass of displaced liquid, which changes the period.
- Where marks are lost
- Research design: using different fluids with no way to measure or quote viscosity. Data analysis: reading the amplitude by eye instead of from video. Evaluation: ignoring that the drag becomes quadratic at higher speed and that the temperature drifts.
- Data
- Needs a video camera or phone, Tracker and glycerol; the main uncertainty is reading the amplitude and the viscosity values from tables.
Damping strength and decay constant of a mass on a spring
Research question. How does the area of a card vane (0 to 100 cm², six values) attached to an oscillating mass-spring system affect the decay constant of its amplitude?
- C.1 Simple harmonic motion
- SL and HL
- Needs care
- Rarely listed
My take. A good, feasible choice with plenty of room for analysis. Keep the damping light so you get enough cycles, and test whether the decay is truly exponential.
Method, physics and where marks are lost+
- Independent variable
- Vane area attached beneath a 200 g mass on a spring: 0, 20, 40, 60, 80, 100 cm² (six values), three runs each.
- What you measure
- Peak amplitude for successive oscillations, taken from video analysis (Tracker) or a motion sensor. Decay constant λ found from the gradient of ln(A) against time.
- Controlled variables
- Mass and spring (same ones throughout); initial amplitude (release from the same 5 cm displacement using a marked stop); vane shape and card thickness (same card, cut to size); air conditions (no draughts, doors shut).
- Physics and graph
- Light damping gives A = A₀e−λt. Plot ln A against t, so the gradient is −λ. Then plot λ against vane area and test for proportionality, reasoning that drag rises with area.
- SL and HL
- SL students can extract λ and describe the trend. HL depth: relate λ to b/2m for a damping force −bv, and examine whether b is linear in area or follows a v² drag law at larger amplitudes.
- Where marks are lost
- Data analysis: reading peaks by eye from video frames, giving noisy ln A; not checking the graph is linear. Research design: amplitude too small to measure past a few cycles. Evaluation: ignoring that drag may not be linear in speed.
- Data
- Spring, masses, card and a phone camera with Tracker; the main uncertainty is peak position from video frame rate and mass wobble.
Does bob mass change pendulum period? A precision test
Research question. Does the period of a simple pendulum of length 0.80 m released from 10 degrees change when the bob mass is varied from 20 g to 200 g in six steps?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Rarely listed
My take. A very common topic and the answer is known in advance, so it scores only if you handle the null result carefully. Add a twist such as a hanging thread of measurable mass or a hollow versus solid bob.
Method, physics and where marks are lost+
- Independent variable
- Bob mass: 20, 50, 80, 110, 150, 200 g brass or steel slotted masses, with five repeats of each.
- What you measure
- Time for 20 oscillations with a light gate or phone video at 60 fps, giving period T = t/20 with uncertainty from the spread of repeats.
- Controlled variables
- Length measured from pivot to centre of mass of the bob, checked after each mass change. Release angle marked on a protractor board at 10 degrees. Same thread and pivot clamp. Bob size kept similar so drag does not change.
- Physics and graph
- T = 2π√(L/g), independent of mass for small angles. Plot T against mass and fit a line: a gradient consistent with zero within uncertainty supports the theory. Better, compare T² against L for several lengths to get g as a second check.
- SL and HL
- SL: show the null result with proper error bars. Top band: quantify how small a mass effect could be detected, and study where mass does matter, such as air drag with a light, large bob, or a heavy thread whose mass adds to the effective moment of inertia.
- Where marks are lost
- Research design: expecting a dramatic trend, using bobs that also change in size, and timing one swing only. Data analysis: no uncertainty in the gradient. Conclusion: saying 'no effect' without stating the range that is consistent with zero. Evaluation: ignoring the length shift when masses are swapped.
- Data
- Stopwatch, clamp stand and masses are enough, but a light gate greatly reduces reaction-time uncertainty.
Does g from a pendulum depend on string length?
Research question. How does the value of g, calculated from the period of a simple pendulum, change as the string length is varied from 0.30 m to 1.20 m in steps of 0.15 m?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Rarely listed
My take. A very common and accessible experiment, so it only earns high marks if you treat it as a test of whether g really is constant and analyse systematic errors carefully. Make it personal by using a location such as a stairwell for long lengths, or by comparing timing with a phone video frame count against a light gate.
Method, physics and where marks are lost+
- Independent variable
- Length of the pendulum, measured from the suspension point to the middle of the bob, at 7 values from 0.30 m to 1.20 m in 0.15 m steps. Each length is set up three times, with the string re-clamped each time.
- What you measure
- Time for 20 complete oscillations measured with a stopwatch or a light gate with timer, repeated 3 to 5 times per length. The period T is the time divided by 20, and g is calculated from g = 4π²L/T².
- Controlled variables
- Release angle kept under 10° by marking a fixed displacement on a protractor or a paper scale behind the bob. Bob mass and size kept identical by using one dense metal sphere. String type kept the same, thin and inextensible, clamped firmly at a fixed point. Same timing method and starting point (the centre of the swing, using a fiducial marker) for every run.
- Physics and graph
- For small angles T = 2π√(L/g). Plot T² against L: a straight line through the origin with gradient 4π²/g gives g from the fit. Also plot the individual g values against L to check whether any trend shows a systematic error, and compare the fitted g with 9.81 m s⁻² using the uncertainty from the gradient (maximum and minimum lines).
- SL and HL
- An SL student can collect the data, plot T² against L and compare the gradient-based g with the accepted value with propagated uncertainties. To reach the top band, add a quantified systematic effect, such as the bob's finite size (physical pendulum correction), the amplitude correction to the period, or the effect of the clamp, and show whether the g against L trend disappears once corrected. HL depth could use the moment of inertia of the bob to derive the physical pendulum period.
- Where marks are lost
- Research design: the RQ asks about variation of g with L, but g is a constant, so a weak design just expects a flat line without explaining why it might not be flat. Data analysis: timing only a few swings, ignoring the reaction time uncertainty, or averaging g values without a graph. Conclusion: stating that g equals 9.81 without a percentage difference tested against the uncertainty. Evaluation: not identifying the systematic errors (length measured to the wrong point, amplitude too large, string stretch), and giving vague fixes such as 'use a better stopwatch'.
- Data
- Needs a retort stand, string, metal bob, metre rule and stopwatch (or light gate); the main uncertainty is the length measured to the bob's centre of mass and human reaction time in timing.
Does sphere size change rolling oscillation on a curved track
Research question. How does the radius of a solid sphere (0.5 to 2.0 cm, 6 sizes) affect its oscillation period when rolling in a curved track of radius 50 cm?
- C.1 Simple harmonic motion
- SL and HL
- Needs care
- Rarely listed
My take. Neat because the prediction is precise, so you can test it. Check the track really is circular before starting, and expect the effect of r to be small but predictable.
Method, physics and where marks are lost+
- Independent variable
- Sphere radius from 0.5 to 2.0 cm, using ball bearings or marbles, measured with vernier callipers. Five period measurements per ball.
- What you measure
- Time for 10 oscillations from phone video or a light gate, divided by 10 to get T. Compare with the predicted T using effective radius R - r.
- Controlled variables
- Same track and surface; small release angle under 10 degrees; same material (steel) where possible; track levelled with a spirit level.
- Physics and graph
- A solid sphere rolling without slipping in a bowl of radius R has T = 2 pi √(7(R - r)/(5g)). Plot T2 against (R - r); the gradient is 28 pi2/(5g). Test whether T is independent of mass.
- SL and HL
- SL students compare T against r and check the trend. Top band work derives the 7/5 factor from rotational energy, which reaches into HL rigid body ideas, and compares gradient with g.
- Where marks are lost
- Research design: the track is not truly circular so the model fails. Data analysis: T versus r is plotted without using R - r. Evaluation: slipping and rolling friction are ignored.
- Data
- Needs a curved track such as a bent rail or a shallow bowl and calipers; the uncertainty is the track shape and timing, so use many oscillations.
Finding the fastest pivot on a swinging rule
Research question. How does the distance d of the pivot from the centre of mass of a 1.00 m rule, varied from 0.05 m to 0.45 m in 0.05 m steps, affect its period for small oscillations?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Rarely listed
My take. A solid classic with a clear model and a satisfying minimum. Add the linearisation and a value of g from the intercept to make it more than a period table.
Method, physics and where marks are lost+
- Independent variable
- Distance d of the pivot hole or clamp position from the centre, 0.05 m to 0.45 m in 0.05 m steps (9 values, 3 sets of 10 oscillations at each).
- What you measure
- Time for 10 oscillations with a stopwatch or phone video, divided by 10 to give T. Predicted T = 2π√((k² + d²)/(g d)), where k² = L²/12.
- Controlled variables
- Amplitude: small, below about 10°, set with a marked angle guide. Pivot friction: a knife edge or a thin nail through drilled holes. Ruler mass: the same rule with nothing attached. Plane of swing: guided to remain in one plane.
- Physics and graph
- Physical pendulum T = 2π√(I/(mgd)), with I = m(k² + d²) by the parallel axis theorem. Plot T²d against d², the gradient is 4π²/g and the intercept is 4π²k²/g. The minimum period occurs at d = k.
- SL and HL
- SL: measure T against d, describe the minimum and compare with a simple pendulum. Top band: linearise to find g and k and check it against L/√12. The parallel axis theorem is an HL idea, but SL students can use it if it is derived.
- Where marks are lost
- Research design: only a few pivots, none close to the minimum. Data analysis: T² against d, which is not linear. Conclusion: no comparison of the predicted minimum. Evaluation: not addressing amplitude, and hole size affecting the pivot position.
- Data
- A metre rule with drilled holes and a stopwatch are enough; timing 10 swings keeps the human reaction uncertainty below 2%.
Large swing angles and the error in measured g
Research question. How does the release angle of a simple pendulum, from 5° to 60° in 5 steps of 5° or more, change the value of g calculated from T = 2π√(L/g) with L = 1.000 m?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Rarely listed
My take. Common at school level but still strong when you fit a correction term and quantify it. Aim for the correction, not just the trend.
Method, physics and where marks are lost+
- Independent variable
- Release angle, 5°, 10°, 20°, 30°, 45°, 60° (6 values), measured with a protractor or from a photo, 3 repeats each.
- What you measure
- Time of 20 oscillations with a stopwatch or a light gate to get T, then g = 4π²L/T². Percentage difference from 9.81 m s⁻² calculated.
- Controlled variables
- Length from pivot to the centre of mass (measured with a metre rule and calipers). Bob mass and size. Pivot type (clamped between two blocks). Number of swings timed.
- Physics and graph
- For small angles T = 2π√(L/g); for larger angles T ≈ T0(1 + θ²/16). Plot g calculated against θ², or T against θ², to show a linear rise in T and the point where the small angle approximation fails.
- SL and HL
- SL: show that g drifts as angle grows and compare to 9.81. Stronger: compare to the series correction and fit it, and use it to correct g at large angles.
- Where marks are lost
- Research design: too few large angles, or timing single oscillations. Data analysis: not propagating length and time uncertainty into g. Evaluation: ignoring damping over 20 swings.
- Data
- Needs a stopwatch, metre rule and a protractor; reaction time is the main uncertainty unless a light gate is used.
Magnetic field near a pendulum bob and its period
Research question. How does the current through a pair of Helmholtz coils (0 to 2.0 A, 6 or more values) affect the period of a pendulum with a magnetic bob swinging between them?
- C.1 Simple harmonic motion
- SL and HL
- Hard data
- Rarely listed
My take. Risky because a non-magnetic bob shows nothing, and voltage is a poor variable, so use current and measured field. Worth choosing only with a magnetic bob, where the result is a real physical effect.
Method, physics and where marks are lost+
- Independent variable
- Coil current, 0 to 2.0 A in steps of 0.4 A, from a variable DC supply, with the current read on an ammeter. The field B is measured with a Hall probe at the bob position.
- What you measure
- Period from the time for 20 oscillations with video or a light gate, then T = t / 20. Repeat 3 times per current.
- Controlled variables
- Pendulum length, measured to the centre of the bob. Amplitude, no more than 5 degrees. Bob mass and magnet orientation. Coil temperature, by limiting run times, and distance from other magnetic material.
- Physics and graph
- For a magnetic bob the extra force adds to the restoring force, so T = 2 pi √(L / geff), with geff depending on B. If the bob is non-magnetic conductive, eddy damping appears instead. Plot 1 / T2 against B, and look at the gradient as a measure of the magnetic effect. Note that a non-magnetic bob will show no change in period.
- SL and HL
- SL: measured period against B and a linear fit if a trend appears. Top band: build a force model for a bar magnet in a uniform field, checked by a Hall probe. Also test a steel or aluminium bob as control. No HL topic is needed.
- Where marks are lost
- Research design: not stating what bob material is used, since the effect depends on it. Data analysis: reporting no change in period without uncertainty analysis. Evaluation: forgetting that Helmholtz coil heating changes the current, and the field not being uniform near the edges.
- Data
- Needs a Helmholtz pair, a power supply, a Hall probe and a magnetic bob; the main uncertainty is that the effect on the period may be tiny.
Mass-spring period and effective spring mass
Research question. How does the period of a vertical steel spring oscillating with hanging masses from 0.100 kg to 0.500 kg vary with mass, and what spring constant and effective spring mass follow?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Rarely listed
My take. Well known and appears often, but the intercept for the spring mass and the static check give it extra depth. Keep one independent variable, mass, and treat the length as a separate follow-up only if you have time.
Method, physics and where marks are lost+
- Independent variable
- Hanging mass: 6 to 8 values from 0.100 to 0.500 kg in steps of 0.050 or 0.100 kg, with the period timed 3 times per mass. A second, optional set uses different numbers of coils (spring cut or springs in series or parallel).
- What you measure
- Time for 20 oscillations measured with a stopwatch, or with a motion sensor for a cleaner signal; period T is found by dividing, then T squared is calculated.
- Controlled variables
- Amplitude: fixed at about 2 cm and kept small. Same spring for the mass series. Release: vertical release without sideways motion. Starting position: timing from the centre of the oscillation using a fiducial marker.
- Physics and graph
- T = 2 pi √((m + ms/3)/k). Plot T squared against m; the gradient is 4 pi squared over k and the horizontal intercept gives the effective spring mass. Compare k with a static extension test using Hooke's law.
- SL and HL
- SL students plot T squared against m and find k. Stronger work finds the intercept and connects it to a third of the spring mass, and checks k from static extension. HL depth could add damping analysis using a motion sensor.
- Where marks are lost
- Research design: two independent variables mixed together. Data analysis: reaction time on only 5 oscillations, and no linearisation. Evaluation: ignoring spring mass and non-vertical oscillation.
- Data
- Retort stand, spring, slotted masses and stopwatch; a motion sensor would improve timing, and the main uncertainty is human reaction time.
Oil viscosity and damping of a swinging pendulum
Research question. How does the viscosity of a range of water and glycerol mixtures, from 1 mPa s to about 500 mPa s, affect the damping constant of a bob oscillating at small amplitude?
- C.1 Simple harmonic motion
- SL and HL
- Needs care
- Rarely listed
My take. Ambitious but very rewarding. Measure the viscosity yourself with a falling sphere, so the whole investigation is your own data.
Method, physics and where marks are lost+
- Independent variable
- Glycerol fraction by volume in water: 0%, 20%, 40%, 60%, 80%, 100% (6 values). Viscosity is taken from published tables for the measured temperature, or found by a falling ball test.
- What you measure
- Amplitude of a pendulum with a submerged bob, filmed at 120 fps with a phone against a scale, and read over 10 or more oscillations. Damping constant is found from the gradient of ln(A) against time.
- Controlled variables
- Same bob, same string length and same immersed depth. Starting amplitude kept small, at about 5 degrees. Temperature of the liquid recorded with a thermometer, as viscosity changes strongly with it. Same container so the wall effects do not change.
- Physics and graph
- Amplitude decays as A = A₀e−γt for light damping, so ln(A) against t is a straight line with gradient −γ. Stokes drag on a small sphere is 6πηrv, so γ should increase with η at low speeds. Plot γ against η. At high damping the motion is no longer oscillatory, which is worth noting.
- SL and HL
- SL: measure γ for each mixture and plot γ against η, describing the trend. Top band: compare the gradient with the value predicted from Stokes' law and discuss where the Reynolds number makes it fail. HL depth: solve the damped oscillator equation and identify critical damping.
- Where marks are lost
- Research design: uncontrolled temperature, and viscosity values taken without matching them to the temperature. Data analysis: reading amplitude by eye without filming. Conclusion: claiming a linear relation when the data curve at low or high viscosity. Evaluation: ignoring drag on the string and buoyancy, which alter the effective mass.
- Data
- Needs glycerol, a tall container, a pendulum, a phone camera and a thermometer; the main uncertainty is the viscosity value at the actual temperature.
Pendulum period when the string wraps round a peg
Research question. How does the distance d of a fixed peg below the pivot, varied from 0.10 m to 0.60 m in steps of 0.10 m on a 0.80 m string, affect the period of a pendulum whose string catches on the peg at the bottom of its swing?
- C.1 Simple harmonic motion
- SL and HL
- Easy data
- Rarely listed
My take. A neat twist on the standard pendulum because the prediction is not a simple power law, so it invites real modelling. Make it yours by testing the model prediction at each peg position and explaining why the residuals look the way they do. The original idea of pivot geometry was vague, and this is the closest measurable version.
Method, physics and where marks are lost+
- Independent variable
- Peg distance d below the pivot: 0.10, 0.20, 0.30, 0.40, 0.50 and 0.60 m (6 values), with the total string length fixed at 0.80 m. Ten timed sets of 10 oscillations at each value.
- What you measure
- Full period T of the two-part swing, found by timing 10 oscillations with a stopwatch or a phone video analysed frame by frame (or a light gate), then dividing by 10. Compared with the period predicted from the two effective lengths L and (L minus d).
- Controlled variables
- Bob mass and size: same steel sphere throughout. Release angle: kept at 8 degrees using a printed protractor sheet and a clamp stop. Total string length: measured with a metre rule from pivot to bob centre each time. Peg diameter: one thin rod used for all runs, so the wrapping radius does not change.
- Physics and graph
- For small angles T = 2π√(L/g). With a peg, half the swing has length L and half has length (L minus d), so T = π√(L/g) + π√((L−d)/g). Plot T against √(L−d) and check for a straight line with gradient π/√g and intercept π√(L/g). Compare g from the gradient with 9.81 m s⁻².
- SL and HL
- SL students can time the swing, plot the linear graph and get g with an uncertainty. Top band work checks the small angle assumption by repeating at two amplitudes and explains any offset from the peg radius. HL depth can come from deriving the two-part period model, discussing how the string bending on the peg changes the effective length, and estimating the correction from the finite bob size.
- Where marks are lost
- Research design: choosing large release angles so the small angle formula fails, or failing to keep the total length fixed. Data analysis: ignoring the uncertainty in timing and plotting T against d, which is not linear. Conclusion: not comparing the measured curve with the derived model quantitatively. Evaluation: not addressing friction at the peg, the string thickness and the bob's finite size, which all shift the results systematically.
- Data
- Needs a retort stand, thread, a steel bob, a thin rod and a stopwatch or phone; the main uncertainty is reaction time, reduced by timing 10 swings and repeating.
Period of a torsion pendulum against mass radius
Research question. How does the distance r of two 100 g masses from the axis (2 to 12 cm, six values) affect the period of a torsional oscillator made from a disc on a steel wire?
- C.1 Simple harmonic motion
- HL topic
- Needs care
- Rarely listed
My take. Worth choosing if you have the apparatus, because the linear T² against r² graph is clean and the intercept gives you something to interpret. Building the rig is the hard part, so test it early.
Method, physics and where marks are lost+
- Independent variable
- Radial position of two identical masses placed symmetrically on the disc: 2, 4, 6, 8, 10, 12 cm from the centre (six values), repeated three times.
- What you measure
- Period T from timing 10 oscillations with a stopwatch or a phone video, with T² then calculated for each radius.
- Controlled variables
- Wire (same length and clamp); mass of each added body (weigh both); angular displacement (start at about 20°, small enough to stay linear); disc and hanging mechanism (unchanged throughout).
- Physics and graph
- T = 2π√(I/κ) with I = I₀ + 2mr². Plot T² against r²: gradient = 8π²m/κ and the intercept gives 4π²I₀/κ. The torsion constant κ follows from the gradient.
- SL and HL
- Rotational moment of inertia is HL (A.4), so this suits HL best. An SL student would need heavy guidance. Top band: compare κ from the gradient with an independent estimate, for example from the wire's shear modulus and dimensions.
- Where marks are lost
- Research design: masses not placed symmetrically or radius measured to the mass edge instead of its centre. Data analysis: forgetting the non-zero intercept from the disc's own inertia. Evaluation: not checking damping or a change of κ with large twist.
- Data
- Needs a steel wire, clamp, disc with marked radii and masses; the main uncertainty is timing and the position of each mass.
Suspension wire thickness and the decay rate of a pendulum
Research question. How does the diameter of a copper suspension wire (0.20 to 1.00 mm, 5 values) affect the damping constant of a 0.50 m pendulum?
- C.1 Simple harmonic motion
- SL and HL
- Hard data
- Rarely listed
My take. Ambitious, and the effect may be hidden behind air drag and clamp friction. Take it on only if you can run for several minutes per trial; otherwise the data will be noise.
Method, physics and where marks are lost+
- Independent variable
- Wire diameter from 0.20 to 1.00 mm, 5 gauges, checked with a micrometer at several points on each wire. Three swings sets per gauge.
- What you measure
- Amplitude against time from phone video and a protractor board, or a light gate for the period; the damping constant is the gradient of ln(A) against t.
- Controlled variables
- Same bob mass and shape; wire length fixed at 0.50 m; starting angle 10 degrees; same clamp and same room, avoiding draughts.
- Physics and graph
- For light damping A = A0 exp(-γ t). Plot ln(A) against t, γ equals minus the gradient. Thicker wires dissipate more energy through bending and clamp losses, so compare γ with diameter (perhaps d4 for bending stiffness).
- SL and HL
- SL students find γ for each wire and plot it against diameter. Top band work proposes a bending stiffness model and considers whether wire or clamp is dominating.
- Where marks are lost
- Research design: thicker wire also alters mass and stiffness, mixing several effects. Data analysis: amplitude is read from video too coarsely. Evaluation: clamp friction is not separated from wire effects.
- Data
- Needs a micrometer and several wire gauges; damping from a wire is very small, so long runs are needed and the uncertainty is large.
Ideas were collected from public lists and published IA titles, merged when they are the same investigation, and rewritten from scratch. “On N sites” counts how many public lists carry the same investigation. How this list was made.
Frequently asked questions
What are good IB Physics IA ideas on simple harmonic motion?
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Good starting points with easy data that few sites list are does bob mass change pendulum period? a precision test, does g from a pendulum depend on string length? and finding the fastest pivot on a swinging rule. Each one gives a straight-line graph from school equipment, which is what the Data analysis and Conclusion criteria need.
Which simple harmonic motion IA ideas are overdone?
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testing t squared against length for a simple pendulum and where the small-angle pendulum formula stops working appear on three or more public lists. They still work, but they need a twist that shows your own thinking.
Can I do a simple harmonic motion IA at SL?
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16 of the 17 ideas use SL physics. The others rely on HL-only content and are marked as HL topics.