Investigation of a simple pendulum

Students investigate factors affecting the oscillation time for a simple pendulum.

Apparatus and Materials

For each student group:

• string, 2 m length
• metre rule
• bob (e.g. hanger with slotted masses, 10 g, or lump of Plasticine)
• Stopclock or stopwatch
• Stand, clamp and boss
• Protractor
• Metal strips used as jaws, 5 cm, 2
• G-clamp

Health & Safety and Technical Notes

Put something on the floor to prevent damage should the mass fall.

Avoid large amplitude oscillations.

Read our standard health & safety guidance

If large masses are used then the stands may need to be clamped to the bench.

Procedure

1. Show a demonstration pendulum and ask students to think about the variables that may affect the time period for one oscillation.
2. Ask students to select one independent variable, collecting a set of data to investigate its effect on the oscillation time.
3. After students have completed an initial investigation and drawn conclusions, ask them to evaluate their method in terms of its accuracy and improve on it.

Teaching Notes

• Given the right attitude, students can really enjoy these investigations. Choose how far to take them, to suit your students’ age and experience. You may need to explain what one oscillation for a pendulum means (motion “there and back again” i.e. moving in the original direction).
• Variables to investigate include:
• The mass of the pendulum bob
• Length of the pendulum (best measured to centre of bob)
• Initial amplitude (angle or displacement).
• The periodic time for a swinging pendulum is constant only when amplitudes are small. Students investigating the effect of bob mass or pendulum length should keep the maximum angle of swing under 5°.
• Timing the oscillation period for various lengths can be quite tedious. You could arrange it so that pairs of students contribute their results to a communal graph and table of results for the whole class.
• A discussion following students’ first attempts at measuring the periodic time might lead to the following ideas for improving their measured value:
• Measure many oscillations to calculate the average time for one oscillation
• Increase the total time measured for multiple swings.
• There will be some measurement uncertainty both when starting the clock and when stopping the clock, dependent on the experimenter’s reflexes in operating the stopwatch (as much as 0.2 s at each time, i.e. totalling 0.4 s ). The percentage of the total time measured which this uncertainty represents will vary. If more swings are counted and the total time is greater, then 0.4 s will be a smaller percentage of that total time. Students could carry out simple error calculations to discover, for example, the effect of a human reaction time of 0.2 s econds on timings of 2 s 20 s and 200 s.
• [You may wish to get them to estimate the human reaction time or measure it as a separate activity. There are many web-based activities freely available.]
• They can improve the accuracy of their measurements by:
• Making timings by sighting the bob past a fixed reference point (called a ‘fiducial point’)
• Sighting the bob as it moves fastest past a reference point. The pendulum swings fastest at its lowest point and slowest at the top of each swing.
• Students can first plot a graph of periodic time, T , against length, l , getting a curve (a parabola). They could try a few quick calculations to see whether the graph to plot is T ,l / T,√T or T² against l rather than just telling them it is T² against l.
• The period of oscillation of a simple pendulum is T = 2π√(l / g ) where:
• T = time period for one oscillation (s)
• l = length of pendulum (m)
• g = acceleration due to gravity (m s^-2
• A graph of T² against l should be a straight line graph, showing that T²  ∝  l. This line may indicate that more readings are needed as the plotted points may be too close together.
• From the graph of T² against l the value of g can be found because the slope of the graph is 4π² /g.