Factors affecting the period of an oscillator

Class practical

The experiment involves isolating and controlling one variable at a time, taking measurements carefully and drawing numerical conclusions by comparing sets of measurements.

Apparatus and Materials

Spring systems
• expendable steel springs, 4
• hanger with slotted masses, 100g
• retort stand base, rod, boss and clamp
• stopwatch or stopclock
• stiff wire
• pliers
Tethered trolley
• dynamics trolleys, 4
• expendable steel springs or rubber bands, 8
• retort stand bases and rods, 2
• G-clamps, 2
• bench space or runway for trolley

Health & Safety and Technical Notes

Spring systems

Use a stiff wire to connect the springs in parallel.

Tethered trolley

The diagram above shows a convenient arrangement. Initially each end of the trolley is tethered by two or three springs in series to allow an oscillation of reasonable amplitude.

Read our standard health & safety guidance

Procedure

Spring systems

1. Students should aim to find out how T, the time for one oscillation, depends on
2. the amplitude, A, of the motion
3. the mass, m, of the load
4. k

Warn the students when varying m, not to use more than 800g, which would damage the spring.

Tethered trolley In this experiment, students should aim to find out how T, the time for one oscillation, depends on

1. the trolley mass, m
2. k

To raise the force constant, further sets of 2 or 3 springs can be added in parallel at each end of the trolley. To raise the mass, trolleys are stacked on the tethered one, or other suitable masses are placed on it.

The spring constant, k, of the system need not be measured in either of the experiments described above. Students need only know that they can alter it by adding further springs to the initial one, either in series or in parallel. If the k for one spring is called 1 unit, k for two springs in series is ½ unit, k for three in series is 13 unit, k for two in parallel is 2 units, etc.

Teaching Notes

• You might choose to have all students, in pairs, doing just one of the two experiments. Alternatively, some pairs of students investigate vertical springs systems while others investigate the tethered trolley arrangement.
• One approach might be to say: "You may assume that the frequency is either directly or inversely proportional to m, or to √ m , or to m³, and that the same applies to variation with k. Do the simplest experiments you can, to decide which functions apply."
  • Students who are skilful and numerate may be able to find the relationships T  ∝  √ m  and T  ∝  1√ k  on their own.
  • Others, however, may need prompting from questions like: "How do you have to change m so that T doubles?" and "How do you have to change k so that T doubles?"
  • Students may be slow to grasp that it is factor changes which are being considered (two times, three times, half, etc.), not numerical changes (1 s longer, 100 g more, etc.). Alternatively, you could give the students the known relationships and ask them to empirically check that they are correct.
• Students should bear in mind the measurement uncertainties in these experiments. For example, when T₁ = 0.98s ±  0.02s, and T₂ = 0.51s ±  0.02s, then T₁ = 2 x T₂, within experimental uncertainty. You may need to review (or introduce) ideas about using a stopwatch, and about repetitive timing events. A mechanical stopwatch may advance in intervals of 0.2 s, and a digital one will probably use intervals of 0.01 s. Human reaction time, though not consistent, is typically 0.2 s. This applies, of course, both when starting and when stopping a clock, so could be as much as 0.4 s in total. With isochronous oscillations, accuracy can be improved by timing as many oscillations as possible, reducing the uncertainty in calculated T.

This experiment has yet to undergo a health and safety check.