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A-level Physics required practicals

Simple harmonic motion — spring and pendulum systems

AQA 3.6.1.3 · RP7

A-level Physics (7408) · Required practical 7 — method, techniques, safety, analysis and uncertainty. Includes errors documented in examiner reports.

Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works

Investigate how period depends on suspended mass for a spring and on length for a simple pendulum, then use linearised graphs to determine the spring constant and gravitational field strength.

Apparatus

  • Clamp stand, boss, clamp, spring and mass hanger with slotted masses
  • Pendulum bob, light string and a second secure clamp
  • Metre rule, set square and electronic balance
  • Fiducial marker for judging the equilibrium crossing
  • Vibration transducer, oscilloscope and suitable connecting leads

Apparatus & techniques (AT)

AT a · analogue measurement

Read spring extension, pendulum length and fiducial positions from analogue length scales.

AT b · digital instruments

Use an electronic balance and the oscilloscope's digital time-base settings to record mass and period data.

AT c · accuracy methods

Time several cycles, repeat readings and measure pendulum length from fixed reference points to improve accuracy.

AT h · signal generator/oscilloscope

Display the vibration-transducer signal on an oscilloscope and obtain the period from repeated trace cycles.

AT i · wave generation/measurement

Generate controlled spring and pendulum oscillations and measure their period while keeping the amplitude small.

Safety

Hazard

A falling mass or toppling clamp stand can injure feet or damage equipment.

Control

Use a heavy base, keep the stand away from the bench edge, limit the mass and place a tray or soft landing beneath the hanger.

Hazard

A pendulum bob can strike a person or nearby apparatus.

Control

Keep the swing small, clear the arc and release the bob without pulling it towards anyone.

Method

  1. 1Secure the stand so it cannot tip. Suspend the spring and measure each added mass, including the hanger, before allowing the system to settle at equilibrium.
  2. 2Displace the mass vertically by a small amount and release it without a push. Use the vibration transducer to turn the motion into an electrical signal and display the repeating trace on the oscilloscope.
  3. 3Measure the time across several complete cycles on the trace — or time them past a fiducial marker at the equilibrium position — and divide by the number of cycles. Repeat for several masses while keeping the spring and initial amplitude unchanged.
  4. 4For the pendulum branch, measure length from the pivot to the centre of the bob. Release the bob from a small angle and measure several periods for each of a range of lengths.
  5. 5Repeat period readings at each setting, record any anomalous run before deciding whether to repeat it, and calculate a mean only from measurements with a stated justification.

CPAC focus (editorial)

This is an editorial study focus, not an AQA mapping of fixed CPAC competencies to this practical.

  • CPAC 2: Editorial focus: choose workable mass and length ranges, control amplitude and define the measured period consistently.
  • CPAC 4: Editorial focus: record raw repeated periods and anomalous runs before calculating means.
  • CPAC 5: Editorial focus: linearise both models, extract k and g from gradients, and evaluate intercepts and uncertainty.

Variables

Independent

Spring branch: suspended mass; pendulum branch: pivot-to-centre length

Dependent

Period of oscillation

Control

  • Spring, hanger and oscillation amplitude for the spring branch
  • Bob, string and release angle for the pendulum branch
  • Release without a push and the same definition of one complete cycle

Results & processing

  • Plot spring period squared, T2, against mass m. The gradient is 4π2/k, so k = 4π2/gradient; a positive intercept can indicate the spring's effective mass or a mass offset.
  • Plot pendulum period squared, T2, against length L. The gradient is 4π2/g, so g = 4π2/gradient.
  • Check that the points cover a useful range and that any intercept is discussed rather than forcing the best-fit line through the origin.

Analysis skills

  • Linearise the spring relation by plotting T2 against m and use gradient = 4π2/k.
  • Linearise the pendulum relation by plotting T2 against L and use gradient = 4π2/g.
  • Interpret a non-zero intercept using zero offsets and the spring's effective mass rather than automatically forcing the origin.

Uncertainty

Sources

  • Oscilloscope time-base resolution and judgement of corresponding points on the trace
  • Scatter caused by release technique and damping
  • Uncertainty in pivot-to-centre length and any spring mass offset

Calculations

  • Use half the range of repeated period values as an estimate of random uncertainty where appropriate.
  • Divide the uncertainty in a multi-cycle time interval by the number of cycles to obtain the uncertainty in one period.
  • Use maximum and minimum acceptable gradients to estimate uncertainty in k or g.

Interpretation

  • Repeats reveal scatter and anomalies but do not remove a systematic length zero error.
  • A larger number of timed cycles reduces percentage timing uncertainty without correcting a biased transducer or scale.

Exam angles

  • Explain why T2, rather than T, is plotted against mass or length.
  • Determine k or g from a best-fit gradient with correct units.
  • Distinguish anomalous-data handling from simply repeating and averaging every value.
  • Explain why the oscillation is timed over several cycles rather than one.

Where students lose marks

Treating repeat readings as though they neutralise an anomalous period rather than identify it.

Fix: Use repeats to expose the anomaly, then investigate the release, trace or length reading that caused it before deciding whether to exclude the run.

  • Examiner report: P3-25 · PDF p. 5

Deleting an awkward period result without first identifying why it is anomalous.

Fix: Keep the raw value, check the trace and release, repeat that setting, then state the evidence used to include or exclude it.

  • Examiner report: P3-20 · PDF p. 3

Using the string length or the bottom of the bob as the pendulum length.

Fix: Measure from the pivot to the centre of the bob and keep the same reference points at every setting.

Improve the method

  • Measure across several cycles on the oscilloscope trace so the time-base reading uncertainty is divided across multiple periods.
  • Use small amplitudes and a consistent release to stay close to the simple SHM model.
  • Use a wide, safe range of masses and lengths to reduce percentage gradient uncertainty.

Source references

  • Specification: AQA 7408 specification §3.6.1.3 · PDF p. 31
  • Specification: AQA 7408 RP inventory — P7 AT a, b, c, h, i · PDF p. 88

Try it — exam-style

Medium
ORIGINAL

A graph of T2 against suspended mass has gradient 3.20 s2 kg−1. Calculate the spring constant.

[2 marks]

Total for this question: 2

Medium
ORIGINAL

A graph of T2 against pendulum length has gradient 4.02 s2 m−1. Determine g.

[2 marks]

Total for this question: 2

Easy
ORIGINAL

Five complete cycles occupy 2.60 ± 0.02 s on an oscilloscope trace. Calculate the period and its absolute uncertainty.

[2 marks]

Total for this question: 2

Questions are written in the style of past AQA papers — never copied from them.

Drill it properly

A-level Physics spec coverage

SHM theory, equations and linked practice across the 7408 specification.

Stuck on simple harmonic motion — spring and pendulum systems?

The graph choice and the uncertainty argument decide most of the marks here — practise both until the method feels automatic.

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