Required Practicals / OCR A / Practical 6
6 A2 PAG 6

Simple harmonic motion (PAG 6)

Investigate SHM using a mass-spring system and a simple pendulum.

Apparatus

  • Helical spring and masses
  • Pendulum (string, bob) and protractor
  • Stopwatch or light gate and datalogger
  • Metre rule and stand

Safety

  • Do not overload the spring.
  • Use small amplitude only (<10 degrees for pendulum).

Method

  1. Mass-spring: hang mass m; displace ~1 cm; time 20 oscillations. Repeat for six masses.
  2. Plot $T^2$ vs m: gradient $= 4\pi^2/k$; find spring constant k.
  3. Pendulum: use length L; small angle <10 degrees; time 20 oscillations. Repeat for six lengths.
  4. Plot $T^2$ vs L: gradient $= 4\pi^2/g$; find g.

Key Variables

Independent Mass m (spring) or length L (pendulum)
Dependent Period T
Controlled Small amplitude; k (spring); g (pendulum)

Analysis and Results

  • Spring: $T = 2\pi\sqrt{m/k}$; $T^2 = (4\pi^2/k)m$.
  • Pendulum: $T = 2\pi\sqrt{L/g}$; $T^2 = (4\pi^2/g)L$.
  • Both $T^2$ graphs should be straight lines through the origin.

Common Errors

  • Timing too few oscillations.
  • Large amplitudes violating SHM condition.
  • Measuring pendulum length to top rather than centre of bob.

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 m graph for a spring has gradient $0.40$ s$^2$ kg$^{-1}$. Calculate k.

Q2 2 marks

A pendulum of length 0.25 m is displaced to an angle of 20 degrees. Explain why the measured period will be slightly greater than $T = 2\pi\sqrt{L/g}$.