Pearson International A Level Physics Core Practical 16: Determine an unknown mass using resonant frequencies

This core practical is part of Pearson's practical-learning programme. The method below is one defensible implementation, not a confidential instruction sheet. Centres may adapt equipment while preserving the scientific purpose, controls, measurements and safety requirements.

Aim and scientific principle

Use the mass dependence of a spring-mass resonant frequency to calibrate and determine an unknown mass.

Begin by translating the title into a testable question. Identify what is deliberately changed, what is measured directly, what is calculated and what must remain controlled. Predict a relationship only after naming the mechanism. A prediction without a reason is weak; a reason without measurable variables cannot guide a practical design.

Apparatus and setup

Use spring or oscillator, known masses, unknown mass, vibration source or displacement sensor, ruler and secure stand. Select every measuring instrument by range and resolution, not by name alone. Draw a labelled scientific setup that shows the working geometry and exactly where readings are taken. Include a control or blank when it distinguishes the target effect from drift, contamination or background response.

Before collecting results, check zero readings, calibration, leaks, alignment or sterility as relevant. Record the instrument resolution beside the first raw-data table. If a digital device displays more digits than its underlying accuracy supports, do not treat every digit as equally certain.

Method

1. Measure or establish the oscillator configuration and determine resonant frequency for several known masses.
2. Keep amplitude small and use a consistent criterion for resonance.
3. Transform the relationship, such as plotting period squared against mass, to obtain a linear calibration.
4. Measure the unknown's frequency or period and interpolate its mass within the calibrated range.

Plan the analysis before starting. This reveals whether an additional measurement is needed for a derived quantity and prevents a completed experiment from lacking a mass, length, concentration, background or calibration value. A method should be detailed enough for another trained student to reproduce, while avoiding decorative steps that do not affect validity.

Variables and controls

• Independent variable: known attached mass.
• Dependent variable: resonant frequency or period.
• Important controls: spring, oscillation mode, amplitude, support, timing method and added carrier mass.