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How does a nearby electrical conductor affect the amplitude of a pendulum(formed by a magnet and thread)?

Background Info / Research A pendulum undergoes simple harmonic motion, that is, it oscillates betweentwo endpoints repetitively. In the diagram below, the endpoints are A and C,and “B” is known as the “fiducial point” or the centre of motion. In a vacuum,a pendulum will oscillate between points A and C constantly, as there are noexternal factors affecting the trajectory of the mass bob. Furthermore, itreinforces newton’s first law of motion “all objects will remain at rest or atuniform motion unless acted upon an external force”

However, within the presence of a magnet, the trajectory of the pendulum will alter, and as aresult, alter its endpoints, amplitude, the speed at which it travels and given that it's not a

vacuum, other external factorssuch as air drag / resistance alsoaffects it.. This is known asDamped Simple Harmonicmotion.

The diagram shows the graph ofthe change in displacement astime progresses, supporting ourbackground information.

Considering the presence of an electromagnetic coil, ithas an magnetic field, and that if a pendulum were toswing closely to it, it will come in contact with the magnetic

field and therefore a change in magnetic flux density in thependulum. Faraday’s law states that, a change inmagnetic flux, will induce an emf which will give rise to acurrent Consequently, Lenz’s law states that thisinduced current will always oppose the originalchange in flux . These currents, known as eddy currents,and utilising Lenz’s law will oppose the change in fluxthat generated them . Hence, applying these laws of

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physics, as the pendulum swings across, it will generate eddy currents which will oppose themotion of pendulum due to the change in flux as it enters the vicinity of the coil and as it leavesthe coil, affecting its speed and thereby its endpoints. Hence, as a result, as time progressesand more oscillations occur, the more eddy currents are created which will counteract themotion and thereby affecting the amplitude.

Factors that contribute to change in flux :- Decreasing the relative distance between the conductor and the bar magnet- Increasing the strength of the bar magnet or the electrical conductor (different

conductors)- The relative motion between the conductor and the magnet

The material of the electrical conductor also affects the amplitude of the pendulum.Ferromagnetic materials (iron) are characterised by possessing a high level of magnetismand still persists after the removal of their magnetic field, and in this context, ferromagnetic

materials will have a noticeably larger effect on the pendulum’s amplitude as more eddycurrents are induced that oppose its motion. Contrastingly, paramagnetic materials such asaluminium, are easily magnetised but loses its magnetic field after they leave an externalmagnetic field. Thus, while it still induces eddy currents that oppose its motion, it will have aseverely weaker effect than ferromagnetic materials but still inhibit the pendulum’s amplitudeover time.

Other key factors that will affect the amplitude of the pendulum include the length of thependulum (in our case, we are keeping this constant so this will not be an issue), as the longerthe length, the further the pendulum falls. The angular displacement (angle at which it is let go)

also takes effect on the period of a pendulum and hence then will affect the amplitude of apendulum (as more eddy currents being produced within the magnetic field region) however,this is negligible for small angle differences and truly takes effect on substantial angle changes.

The formula for the period of a pendulum is ), so we can see thatT π( = 2 √l g

gravitational force also plays an effect but the investigation is conducted at the same place so itis not an issue.

Investigation OutlineThe main purpose of this experiment is to investigate the effect of an electrical conductor

(copper sheet) on an pendulum's amplitude over time. As such, we are changing the number ofoscillations (independent variable) and measuring the amplitude of the pendulum (the anglebetween the normal and the endpoints) whilst keeping others factors as controlled such as theangle of release, same conductor, same bar magnet etc.

Aim : To investigate the effect of an electrical conductor on the pendulum’s amplitude over time.

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Hypothesis : As the number of oscillation increases, the amplitude of the pendulum willdecrease faster when there is no presence of an electrical conductor. This is due to thegeneration of eddy currents, which will oppose the motion (slowing it down), decreasing theamplitude as a result.

Independent Variable Dependent Variable Controlled

Number of oscillations (e.g4,6,8,10 oscillations)

Amplitude ( ° c) Retort StandStringPosition of the Electricalconductor (Copper)Material of the Electricalconductor (Copper)Sticky tapeStop watchSame magnet

Angle of release

Equipment:- 30cm string x 1- Bar Magnet x1- Electrical conductor (Copper sheet) x 1- Retort stand x 1- Sticky tape x 1- Protractor x 1- Phone (Slow motion Camera)- Marker pen x 1

Justification : The 30cm string was an arbitrary number selected, not too long but not too short, just the right size in order to demonstrate the effect of an electrical conductor and its motion.The magnet , attached to the string is required as our investigation revolves around the effect ofthe amplitude of the pendulum and the electrical conductor. In a similar vein, the electrical

conductor (copper sheet) is needed as our investigation revolves around the presence of anelectrical conductor and its effect on the pendulum’s amplitude. The retort stand allows themotion of the pendulum to be in almost simple harmonic motion, allowing it to oscillate betweentwo points instead of it moving in an erratic motion. Sticky tape is used due to minimise anyexternal factors, such as the string’s movement being affected because the string was not tiedproperly into the retort stand, and sticky tape minimises this factor as it keeps it in place. Aphone is required as it records the whole procedure and can be playbacked to record our results

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for the appropriate sections. The protractor is needed to measure the angle it creates betweenthe endpoint and the normal. Marker pen to mark the starting position which will be used forsubsequent experiments.

Risk assessment

Risk How to prevent / minimise

The pendulum swinging and hitting anindividual in its trajectory and causing pain

When conducting the experiment, stand30cm away from the pendulum's trajectory toensure there is no physical contact.

The retort stand falling out of the table andcausing injury to an individual

Ensure that prior to the experiment, the retortstand is a fair distance away from the edge ofthe table so it won’t fall down.

The magnet falling out of its attachment (fromthe thread and retort stand) and hittingsomeone causing injury

Ensure that all equipment is properlytightened and secure prior to conducting theexperiment.

Method : 1. Set up the equipment shown in the diagram, making

sure the camera is focused within the pendulums rangeof motion2. Align the pendulum 60º from the normal which will bethe starting position.3. Start recording in slow-motion.4. Release the pendulum from the starting position.5. Stop recording video after 10 oscillations, or until thependulum stops swinging.6. Playback the video to obtain results.7. Record the amplitude created by the thread, from theprotractor each time the pendulum completes 2,4,6,8,10oscillation (where amplitude is the angle formed between the normal and endpoints).8. Repeat steps 3-7 two more times for reliability.9. Take the average for the results to ensure greater reliability10. Repeat steps 1-9 without the conductor for the controlled experiment11. Plot the graph, number of oscillations (x-axis) vs amplitude (y-axis)12. Repeat the entire experiment for greater reliability, range of results and more accurateaverages.

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Presence ofan Electricalconductor(Coppersheet)

Number ofOscillations

Amplitude ( ° )

Trial 1 Trial 2 Trial 3 Average

YES 2

4

6

8

10

Presence ofan Electrical

conductor(Coppersheet)

Number ofOscillations

Amplitude ( ° )

Trial 1 Trial 2 Trial 3 Average

NO 2

4

6

8

10

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Bibliography:D. Paradics (Date N/A), “Ferromagnetism and Paramagnetism” (Internet),http://www.physlink.com/Education/AskExperts/ae595.cfm (accessed 14th march, 2016)

Author N/A ( Date N/A), “Oscillations” (Internet)http://teacher.pas.rochester.edu/phy121/lecturenotes/Chapter15/Chapter15.html accessed 14thmarch 2016)

Author N/A (Date N/A) “Simple harmonic motion” (Internet)https://en.wikipedia.org/wiki/Simple_harmonic_motion (accessed 14th march 2016)

Author N/A (2011) “Lenz’s law on electromagnetic induction” (internet) Author N/A (Date N/A) “Exploring pendulums”http://sciencenetlinks.com/lessons/exploring-pendulums/ (accessed 15/03/16)Gale, T. (2006) Oscillation [Internet]. Available from:<http://www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-4/Oscillation.html (accessed14th march 2016)http://www.electrical4u.com/lenz-law-of-electromagnetic-induction/ accessed 14th march 2016

Author N/A (2011) “Faraday’s law on electromagnetic induction” (Internet)http://www.electrical4u.com/faraday-law-of-electromagnetic-induction/ accessed 14th march2016

Author N/A (Date N/A) Doubochinski’s pendulum (Internet)https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Doubochinski_pendulum.svg/250px-Doubochinski_pendulum.svg.png (accessed 14/03/16)

Book Andriessen, M., & Pentland, P (2008) Physics 2 Third edition. Published by John Wiley & Sons Australia, Ltd 42 McDougall Street, Milton, Qld 4064.