Required Practicals / Edexcel / Practical 10
10 A2 CP10

Simple harmonic motion: mass-spring and pendulum (CP10)

Investigate SHM by measuring the period of a mass-spring system and a simple pendulum as mass or length is varied.

Apparatus

  • Helical spring and set of masses
  • Simple pendulum (string and bob) and protractor
  • Stopwatch or light gate
  • Metre rule and stand

Safety

  • Do not overload the spring past its elastic limit.
  • Keep pendulum amplitude small for the SHM approximation to hold.

Method

  1. Mass-spring: add mass m to the spring. Displace ~1 cm and time 20 oscillations; find $T = \text{total time}/20$.
  2. Repeat for at least six masses. Plot $T^2$ vs m; gradient $= 4\pi^2/k$.
  3. Pendulum: set length L (pivot to centre of bob). Displace <10 degrees and time 20 oscillations.
  4. Repeat for at least six lengths. Plot $T^2$ vs L; gradient $= 4\pi^2/g$.
  5. Calculate k (spring) and g (pendulum) from the gradients.

Key Variables

Independent Mass m (spring) or length L (pendulum)
Dependent Period T
Controlled Amplitude <10 degrees (pendulum); Spring constant k (spring method)

Analysis and Results

  • Spring: $T^2 = (4\pi^2/k)m$. Gradient $= 4\pi^2/k$.
  • Pendulum: $T^2 = (4\pi^2/g)L$. Gradient $= 4\pi^2/g$, hence $g = 4\pi^2/\text{gradient}$.
  • Both graphs must pass through the origin; curvature indicates SHM conditions are not met.

Common Errors

  • Timing too few oscillations, increasing percentage uncertainty in T.
  • Measuring L to the top of the pendulum bob rather than its centre of mass.
  • Using large amplitudes for the pendulum, causing the period to increase beyond the SHM value.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q1 3 marks

A $T^2$ vs L graph for a pendulum has gradient $3.97$ s$^2$ m$^{-1}$. Calculate g.

Q2 2 marks

A student includes the mass of the spring when plotting $T^2$ vs m for a mass-spring system. Explain how this affects the graph.