Oscillation
Forces and Motion

Oscillations

for 14-16

Anything that vibrates, in other words shows a rhythmic, repetitive motion around an equilibrium position, may be considered an oscillator.  Objects large and small can show such behaviour; for example, electrons in the quartz crystals of watches and clocks, metal structures loaded cyclically (e.g. bridges or aircraft wings), a car bouncing on its suspension, or the larynx in the human voice-box

These experiments enable students to see various oscillators in action, investigate factors that affect their periodic time and represent the motion graphically. They are suitable for students at introductory and intermediate levels of study. For students at advanced level, see also the related collection Simple Harmonic Motion.

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Introduction to oscillations

Oscillation
Forces and Motion

Introduction to oscillations

Practical Activity for 14-16

Class practical

A circus of experiments involving repetitive events, to introduce the concept of oscillation.

Apparatus and Materials

Station A:

  • Oscilloscope with a slow time base

Station B: A rubber ball bouncing

  • rubber ball

Station C: A scaler counting regular pulses

  • signal generator
  • scaler
  • 4mm leads, 2

Station D: A scaler counting slow, random counts from a GM tube

  • scaler/counter
  • GM tube holder
  • thin window GM tube

Station E: A rotating turntable

  • motor-driven turntable
  • card, adhesive tape
  • wire

Station F: A watch or clock ticking

  • stopwatch or stopclock

Station G: A slow-running flashing neon circuit

  • h.t. power supply
  • resistance substitution box, 1 MW
  • capacitor, 1 mF 500 V
  • clip component holder 2
  • neon lamp and m.e.s. holder
  • 4 mm leads

Station H: Dripping water

  • burette, stand, and beaker

Station I: Bar magnet suspended over another magnet

  • cylindrical magnet
  • horseshoe magnet
  • retort stand base, rod, boss, and clamp
  • nylon fishing line

Station J: Large-amplitude pendulum

  • turntable clamped vertically (or large gyroscope)
  • boss (or small G-clamp)
  • retort stand base, rod, and boss

Station K: Air track vehicle running between elastic barriers

  • air track with rubber band barriers at both ends, and blower
  • air track vehicle

Health & Safety and Technical Notes

Station A:
Set the time base at 100 ms cm-1 and the stability control at maximum.

Station B: The ball must bounce gently on a hard surface.

Station C: Set the signal generator to give square waves at about 100 Hz. Connect the high impedance output terminals to the unpolarised scaler input. Increase the output voltage slowly until the scaler counts regularly.

Station D:
Set up the apparatus to show the slow, random background counts from the GM tube.

Station E:
Tape a short piece of wire to the turntable and fix the card so that the wire just touches it as the turntable rotates.

Station F:
If necessary, set up a microphone, amplifier and loudspeaker so that the clock ticking is audible.

Station G:
Connect as shown below.

Station H:
Arrange the burette flow rate so that water drips slowly from it and is roughly steady over short times, but decreases over long times.

Station I:
Hang the bar magnet on nylon line so that it’s horizontal and lies just over the poles of the horseshoe magnet which rests on its back. NOTE: If you attach a small piece of mirror to the suspension, students could also observe the oscillations by optical means.

Station J:
Clamp the turntable with its axis in a horizontal orientation, so that the turntable turns in a vertical plane. Clamp the boss (or G-clamp) onto the edge of the turntable so that the system can be made to execute large-amplitude oscillations about the lowest position of the boss.

Station K:
Set up elastic band barriers across the air track, about 0.5 m apart, so that the vehicle rebounds between them with little loss of energy.

Read our standard health & safety guidance


Procedure

  1. Carefully observe the motion at each station.  In some cases it will be important to time the oscillations. Afterwards, in pairs, discuss the following questions.
  2. How could you tell if an event repeated regularly? Use a clock? How would you know that the clock ticked off equal time intervals? What would be observed if pairs of these repetitive events were compared with each other for rate and for regularity? Which of these events count as clocks? Which are good clocks?

Teaching Notes

  • Set up a suitable circus of experiments, selecting from those listed, so that the class can consider a good range of repetitive events. Make sure to include a few that do not repeat regularly (stations B, D, H, I, J, K). You might also include
  • a ball rolling on curved tracks from examples of simple harmonic motion


    and/or

    Broomstick pendulum


  • When appropriate, facilitate a whole class discussion, basing it on the pair discussions which have taken place.  In general, oscillation involves going back and forth repeatedly between two positions or states.
  • Which stations (systems) produce isochronous oscillations (good timekeepers)? Students might use clocks at home to test their own pulse rates for regularity. (Galileo used his pulse to test a pendulum, or so the story goes.)  Ask whether irregularity matters - is it possible to use radioactive decay as a clock? (Some students may have heard of radiocarbon dating.) You might also refer to modern time standards and to astronomical methods of time measuring. And you might also ask more philosophical questions, such as "Could time run backwards?" and "Would we know if it was doing so?" The direction of time for an elastic collisions, for example, is indistinguishable, but an arrow of time is suggested by the concept of entropy and the 2nd law of thermodynamics.

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

Up next

Frequency of a ticker-timer

Oscillation
Forces and Motion

Frequency of a ticker-timer

Practical Activity for 14-16

Class practical

This develops the idea of frequency, and explores accuracy of measurement.

Apparatus and Materials

For each student group

  • Ticker-timer with power supply unit
  • Ticker-tape
  • Stopwatch or stopclock

Read our standard health & safety guidance


Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Pull a tape steadily through the ticker-timer for a measured amount of time, such as 10 seconds. The dots should be just far enough apart for you to count them.
  2. Count how many dots were made in the measured time.
  3. Work out how many dots were made in each second. That is the frequency of the ticker-timer.
  4. Repeat this at least twice again. Do you get the same answer each time? How can you make your answer for the frequency as accurate as possible?

Teaching Notes

  • The frequency for most types of ticker-timer is that of the mains, but don't tell pupils this until they have completed the exercise.
  • Ways of achieving an accurate result might include good experimental technique (such as starting and finishing the ticker timer and the timing together), and repeated results allowing calculation of an average.
  • When they are using a ticker-timer to analyze motions, students need to know the time interval between each dot. This time is the inverse of frequency. Mains frequency is 50 Hz, so the time interval between each dot is 1/50 s = 0.02 s .
  • Make sure that they count intervals and not dots. The first dot is effectively 0 on a scale of time.

This experiment was safety-tested in March 2005

Up next

Earthquakes in the laboratory

Oscillation
Forces and Motion

Earthquakes in the laboratory

Practical Activity for 14-16

Demonstration

Buildings in earthquake zones need to be designed with modes of vibration and resonance in mind.

Apparatus and Materials

  • Signal generator
  • Vibration generator
  • Leads
  • Materials for building tower (e.g. drinking straws, spaghetti, K'nex, sticky tape, blu-tack, glue gun)
  • Forcemeter, reading up to 10 N
  • Ruler
  • Electronic balance
  • Earthquake table

Health & Safety and Technical Notes

Hammerite paints use xylene as the solvent. When painting just one earthquake table, work in a well-ventilated area, e.g. close to an open window. If more than one table is painted on the same day, work out-of-doors.

Read our standard health & safety guidance


For construction details of the earthquake table see apparatus entry.

Procedure

  1. Students design and build their own tower structures for testing, preferably tall and flimsy. Mount the tower on the earthquake table.
  2. Set the signal generator at a low frequency (a few Hz) and observe the resulting vibrations of the tower as the frequency is gradually increased.

Teaching Notes

  • Points you could discuss:
    • Qualitatively, the phenomenon of resonance: at certain distinct frequencies, vibrations build up to a large amplitude.
    • Modes of vibration: at one frequency all parts of the tower move in phase (all in the same direction at the same time) and at other frequencies some parts move in one direction while other parts move in the opposite direction.
    • In an earthquake zone, it is important to design tall buildings in such a way as to avoid resonance. The frequencies that make the structure resonate must not be the same as typical frequencies of earthquake waves.
  • Students may then explore factors affecting the resonant frequencies of their structures.
  • They could also use a simple mathematical model to predict the lowest resonant frequency of their tower, and compare this with the measured frequency.
  • A vibrating tower of mass m , height h and stiffness k can be modelled, mathematically, as a single mass m mounted at a height h above the base on a massless support of stiffness k. The structure resonates at frequency f = 1/T where T = 2π √(k/m)
  • The stiffness of the tower can be measured by attaching a forcemeter at height of about 2 h /3 above the base and measuring the force, F, needed to produce a horizontal displacement x. Then k = F/x.

This experiment comes from University of York Science Education Group:

Salters Horners Advanced Physics©


Diagrams are reproduced by permission of the copyright holders, Heinemann.

This experiment was safety-tested in April 2006

Up next

Investigating energy transfers in a pendulum

Conservation of Energy
Energy and Thermal Physics | Forces and Motion

Investigating energy transfers in a pendulum

Practical Activity for 14-16

Demonstration

When a pendulum is displaced, it stores energy gravitationally due to its increased height. When subsequently released, this energy is stored kinetically. This datalogging experiment explores the relationship between these changes to the ways that energy is stored.

Apparatus and Materials

  • Light gate, interface and computer
  • Pendulum
  • Stand, clamp and boss
  • Ruler in clamp
  • Micrometer
  • Electronic balance

Health & Safety and Technical Notes

Read our standard health & safety guidance


Set up the apparatus so that the stationary pendulum bob hangs exactly in front of the light sensor, interrupting the light beam.

Connect the light gate via an interface to a computer running data-logging software. The program should be configured to obtain measurements of speed, from which energy stored kinetically can be calculated (by hand or by the program). These are derived from the interruption of the light beam by the pendulum bob: this moves a distance equal to its diameter during the interruption time.

The internal calculation within the program requires the mass and diameter of the bob to be entered into the software, so that the velocity of the bob and energy stored kinetically are calculated. Measure the diameter using a micrometer. Measure the mass using an electronic balance with a sensitivity of 0.01 g. Accumulate the series of results in a table. This should also include a column for the manual entry of displacement height measurements, taken from the ruler.

Procedure

    Data collection
  1. Displace the bob so that it is raised 1.0 cm above its rest height as shown above. Hold the bob against the ruler. Note the reading for the point of contact which is on a level with the centre of the bob. Release carefully and allow it to perform ONE swing to and fro. This should produce two lines of data in the table, corresponding to the forward and back parts of the swing. Repeat this five times. The table shows ten values.
  2. Enter 1.0 cm in the 'change in height' column.
  3. Repeat this procedure for heights of 2, 3, 4 and 5 cm.
  4. Analysis
  5. Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the increase in values of energy stored kinetically as the change in height is increased.
  6. Investigate the relationship between energy stored kinetically and change in height more precisely by plotting an XY graph of these two quantities. (Y axis: energy stored kinetically; X axis: change in height.) This usually gives a straight line indicating proportionality. Use a curve-matching tool to identify the algebraic form of the relationship.
  7. The change in the energy stored gravitationally depends in direct proportion upon the change in height. Therefore, the straight line graph indicates that energy stored kinetically gained is proportional to change in energy stored gravitationally.

Teaching Notes

  • Students can add a further column to the table, to calculate the change in energy stored gravitationally from the change in height, using m g Δh. Care is needed with units. In view of the small values of energy, it may be useful to calculate energy values in millijoules. Calculation of changes to the energy stored gravitationally should yield values numerically the same as the corresponding energy stored kinetically. This would support the law of conservation of energy.
  • If the results are less than convincing, discuss the potential sources of error. Prime suspects must be the measurements performed using the ruler, micrometer and scales.

This experiment was submitted by Laurence Rogers, Senior Lecturer in Education at Leicester University.

This experiment was safety-tested in May 2006

Up next

Investigation of a simple pendulum

Oscillation
Forces and Motion

Investigation of a simple pendulum

Practical Activity for 14-16

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 T 2 against l rather than just telling them it is T 2 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 T 2 against l should be a straight line graph, showing that T 2  ∝  l. This line may indicate that more readings are needed as the plotted points may be too close together.
  • From the graph of T 2 against l the value of g can be found because the slope of the graph is 2 /g.

Up next

Factors affecting the period of an oscillator

Period
Forces and Motion

Factors affecting the period of an oscillator

Practical Activity for 14-16

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 m 3, 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.

Up next

Oscillations and clocks

Period
Forces and Motion

Oscillations and clocks

Teaching Guidance for 14-16

Isochronous oscillators, from the pendulum to the precise oscillations of a caesium atoms in an atomic clock, have an obvious practical use in the measurement of time. But there is more to time than making accurate clocks.

The longitude problem

Early navigators could measure latitude (from the altitude of the sun at noon) but they had to rely on ‘dead reckoning’ to find longitude. Between the 15th and 17th centuries there was huge growth in European trade based on shipping. Accurate and reliable navigation at sea became vitally important, because failing to identify a ship's position near land could cause a shipwreck and, with it, the loss of not only cargo but also sailors’ lives. In 1707 the British Parliament passed The Longitude Act, which offered a substantial cash reward to anyone who could demonstrate a way of accurately determining longitude at sea.

A clock offers one way of finding longitude. If sunrise occurs six hours late or early, one has travelled a quarter of the way round the Earth. This means an error of one minute in time makes a navigational error of nearly thirty kilometres at the equator.

In the middle of the eighteenth century, John Harrison solved the longitude problem by making a sea watch (called H4) that would keep good time, despite a ship’s rolling with ocean waves and despite changes in temperature. Between 18 November 1761 and 21 January 1762 Harrison's sea watch was taken on a voyage from England to Jamaica. On arrival, it was tested and found to be in error by only five seconds after its voyage of 81 days. It was possible to test Harrison’s watch against Jamaica time by sighting the Sun at its highest point in the Jamaican sky, which occurs exactly at noon.

The full John Harrison story is told in Dava Sobel’s book Longitude. A brief summary of Harrison’s work on sea-going clocks is freely available online:

Royal Museums Greenwich website


The quartz clock

In the 1930s a new type of clock started to replace the most accurate pendulum clocks as a standard for measuring time. This was the quartz crystal clock. A quartz crystal will vibrate elastically with a natural period of its own, just like a tuning fork. In this case, however, electrical charges constantly build up and die away on its surface in time with the vibrations. It is this effect, the piezoelectric effect, which makes it so easy both to keep the crystal vibrating and to use the vibrations to control the frequency of electrical oscillations in other circuits. It is these electrical oscillations, accurately controlled by the vibrations of the quartz crystal, which drive the hands of the clock or control its display.

Suppose two quartz clocks are adjusted to read exactly the same time and then left to run without adjustment. Comparisons of their time readings at various times later have indicated a difference of no more than 0.0005 s econd per day over a period of a week or so. This suggests that a quartz clock will measure a time interval of 1 day, or 86 400 seconds, to within 0.0005 s econds; an accuracy of better than 1 in 108. This is ten times better timekeeping than the best pendulum clock.

Quartz clocks were initially developed in response to the demand from scientists and engineers for more and more precise time standards, for the purposes of radio communication, navigation, and pure research. It was also in response to this demand that the atomic clock was developed in 1954.

The atomic clock

Atoms can emit and absorb energy only at very sharply defined frequencies. Provided a suitable atom is chosen, they can be used to control the frequency of radio waves from an electronic oscillator. In 1958 a clock, based on a beam of caesium atoms, was successfully constructed on this principle. The electronic oscillator is controlled by a quartz crystal whose vibrations are in turn controlled by the effect on the beam of caesium atoms of radio waves produced by the oscillator.

As in the case of the quartz clock, it is these accurately maintained electrical oscillations which ultimately drive the clock. Comparison of the timekeeping of two of these clocks showed that atomic clocks could be relied upon to an accuracy of 1 part in 1011 over an apparently indefinite period of time. To put this in a slightly different way, this meant that they could be relied upon to within 1 second in 3 000 years!

In 1964 the international standard second became based on the atomic clock. One second was defined as 9,192, 631,770 cycles of the standard caesium-133 transition.

Global positioning

Today we take for granted that a smartphone can be located to within less than 10 metres, using time signals from a global network of artificial satellites which carry synchronised atomic clocks. GPS satellites continuously transmit their position and current time (accurate to about 14 nanoseconds).

About time

Particle physicists study fundamental particles in the Universe. Influenced by both Newton and Einstein, they are concerned not only with measuring time accurately but also with fundamental questions, such as these: ‘What is time?’, ‘Does time run steadily?’, ‘Could time run backwards?’ and ‘Would we know if it did?’

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