## Coupled Pendulums

December 2, 2011

by:  Martin Sagendorf

One Pendulum…

Is interesting, but…

Two Pendulums…

Are much more interesting.

But Only If…

They are coupled together.

An Easy Way Is To…

Couple them at their pivot points.  This is accomplished by hanging the two pendulums from a horizontal string.

There Are…

Many illustrations of coupled pendulums on the web; search for ‘coupled pendulums’ – but the fine points of making a really successful demo are rarely discussed… so before we start:

Some Guidelines:

-       Make the pendulums absolutely identical: both the rod lengths and the mass values (the lengths are measured from the pivot points to the C.G. of the masses)

-       Use rod lengths of at least 1/3 meter (13”) – so the pendulums don’t swing too quickly

-       Use masses of at least 75 g (1 oz) – to provide a long swing time

-       Space the vertical supports for a horizontal string length of 500 to 600 mm (20 to 24 in.) – weighted or clamped-down ring stands will work – and will work especially well if their top ends are joined by a solid bar to minimize vibrations

-       The string should be fairly taunt – for example:  a 13 to 15 mm (1/2 to 5/8 in.) droop in the center with two 75 g masses hanging 100 mm (4 in.) apart

-       Use pendulum spacings of 75 to 125 mm (3 to 5 in.) – experiment for good results

-       For the best results, symmetrical setup spacing is critical – try to achieve positions symmetric within 4 mm (1/8 in.)

-       When pulling a pendulum to the side, two things are very important: first, don’t pull it too far (a mass rise of 75 mm (3 in.) is fine); second, the pendulum must be pulled at precisely a right-angle to the string

-       For the following exercises, when two pendulums are raised, they should be raised to the same heights

With Two Identical Pendulums:

Center the two pendulums with the pair spaced about 100 mm (4 in.) apart

-       (A.)  Raise and release one pendulum

Question:  What happens?  Why?

-       (B.)  Raise (on opposite sides) and release both pendulums

Question:  What happens?  Why?

With Three Identical Pendulums:

Center the three with a space of about 75 mm (3 in.) between each

-       (C.)  Raise and release the center pendulum

Question:  What happens?  Why?

-       (D.)  Raise and release one of the outer pendulums

Question:  What happens?  Why?

-       (E.)  Raise (on the same side) and release both outer pendulums

Question:  What happens?  Why?

-       (F.)  Raise (on opposite sides) and release both outer pendulums

Question:  What happens?  Why?

So Far…

We have dealt with identical pendulums… but what happens if we:

-       (G.)  Make a pendulum with a greater mass (but the same length) and use it in place of one of those

above

Question:  What happens?  Why?

-       (H.)  Make a pendulum just slightly longer (say, 20%) than one of the three and use it in place of one of

the pendulums above

Questions:  What happens?  Why?

In Action:

Construction Notes:

-       The horizontal string must be firmly attached (tied, hooked, or taped) to the vertical rods

-       The pendulum rods are made from coat hanger wire or from welding rod

-       Hooks are formed in the pendulum rods using a pair of pliers

-       The masses can be any object that can be affixed to the rod – preferably an object through which a hole can be drilled and, for easy identification during demonstrations, the masses should be different colors

In This Apparatus:

-       Length of horizontal string = 600 mm (23-1/2”)

-       Length of pendulum rods (from inside hook to far end) = 440 mm (17-7/16”)

-       Diameter and material of pendulum rods = 1/8” brass welding rod

-       Thread on end of pendulum rod = 6-32 for a length of ¾ in. (Note 1)

-       Nuts = brass 6-32 knurled (2 per rod)

-       Small mass = 5/8” x 2-1/16” steel rod (75 g) – 3 required (Note 2)

-       Large mass = 1” x 1-3/4” steel rod (175 g) – 1 required (Note 2)

-       Distance from inside of pendulum rod hooks to the centers of masses = 400 mm (15-7/8”)

Note 1:  A No. 6 screw diameter is 0.138”. – the 1/8 in. welding rod is 0.013” less – this is OK

Note 2:  Drilled thru No. 29 (0.136”)

A Comment on Dimensions:

The overall dimensions are not critical, but the apparatus should be large enough to be easily viewed in a classroom setting.

A Definition:

These are ‘Simple Pendulums’ because they are not ‘ideal’: i.e. their masses are not concentrated at single points and the restoring force is not a constant – however they do exhibit ‘Simple Harmonic Motion’.  This motion is an approximation at small angles – it is sufficiently accurate for our purposes.

And Further:

The details of Harmonic Motion and Simple Harmonic Motion are fascinating – the details of both can be found in any physics textbook.

‘Resonance’ is defined as the building up of large vibrations by the repeated application of small impulses whose frequency equals one of the natural frequencies of the body – in this case, a pendulum.  Identical pendulums are required to provide maximum energy transfer.  The mechanical energy is transferred by the ‘pulls’ on the supporting string – this is rather like a child’s swing where ‘pushes’ applied at the correct times will ‘add’ and act to increase the swing amplitude.

In Summary:

These demonstrations provide vivid illustrations of energy transfer between two and three resonant bodies.  Even better, additional pendulums, various masses, and variations of excitation will provide more interesting demonstrations and bases for experimentation.

Marty Sagendorf is a retired physicist and teacher; he is a firm believer in the value of hands-on experiences when learning physics.  He authored the book Physics Demonstration Apparatus.  This amazing book is available from Educational Innovations, Inc. – it includes ideas and construction details for the creation and use of a wide spectrum of awe-inspiring physics demonstrations and laboratory equipment.  Included are 49 detailed sections describing hands-on apparatus illustrating mechanical, electrical, acoustical, thermal, optical, gravitational, and magnetic topics.  This book also includes sections on tips and hints, materials sources, and reproducible labels.

## Reinventing Morse: A Case in Educational Design and Teacher Tips

March 25, 2011

by:Benett Harris

If you are a science teacher who has ever taught a physical science class or attended a physical science workshop then you’ve probably done the activity where you wrap a piece of magnet wire around a nail and use it to make a paper clip or another flap of metal move in response to an electrical current flowing in the wire.  This experiment is often called “building a telegraph” and its a good way to illustrate electromagnetism.  The experiment usually goes over well with students, but from experience I’ve found that this simple activity has a lot of stumbling blocks for younger kids and have always thought that it should be possible to teach MORE with your half hour or less activity time.  To that end I’ve created the “Reinventing Morse: Build your own Telegraph” science kit.  This article will explain some of my educational design choices for the kit and give teachers or anyone using the kit for educational purposes a few tips to help them in the classroom.

Fun Fact: Even though making a piece of metal slap into another piece of metal using an electromagnetic field makes a click, this kind of simple apparatus is not actually a telegraph sounder.  To be a true telegraph sounder the device must be capable of making a click on both ends of its travel.  This is how a telegraph operator can distinguish dots from dashes, by noting the time difference between the up and down click’s for each “bit” of code that comes through.  Reinventing Morse is designed to operate as a real sounder because the arm makes a click on both ends of travel.

The First Problem With the Traditional Wire and Nail Experiments:

Magnet wire is simply copper wire that has a small diameter (a large gauge) and is coated with a varnish enamel that insulates it so that adjacent turns of wire won’t short together when wound closely into a coil as in an electromagnet.  Any teacher who has worked with kids and magnet wire will tell you that there are two problems with magnet wire.  Firstly, it’s difficult to remove the varnish so that the ends of the wire may be connected into a circuit.  The best way to do this is to use a knife but obviously this is problematic for elementary or younger students, and so sand paper is usually the next alternative.  The fact that most magnet wire is coated in a varnish that is the same copper color as the copper wire underneath means that its hard to visually inspect a wire to see that its ends are properly stripped or to notice when other areas of the wire are stripped and might short out if brought into contact with another wire.  Secondly, magnet wire’s small diameter makes it hard to wind a nice/clean coil with each turn beside the previous one.  I’ve seen a lot of student and even teacher wound coils that were more like a wad of wire than a neat and efficient coil.  The wire also kinks very easily and can break once its been kinked or twisted.  The result of these two problems is usually more time spent on troubleshooting continuity in a circuit or rewinding a coil than in actually performing an experiment and making observations.  (Granted, troubleshooting can be an important part of a science experiment too).

Magnet wire also has a third limitation in the classroom and that is expense.  It is usually difficult to recycle the wire for future experiments or between class periods because it kinks and breaks easily.  It also usually costs more per foot to replace than other kinds of wire.

To solve these problems with my Reinventing Morse kit I decided to make the kits work using ordinary hookup wire.  Hookup wire usually has a steel core (less expensive than copper) and is coated with a plastic insulator that is clearly a different color than the wire making stripping much easier.  It also hand winds into a coil a little easier and a little more neatly.

Teacher Tip: To improve coil winding (for neater more efficient coils) I also built in a coil winding arbor into the telegraph sounder mechanism.  This arbor works along with the coil winding bobbins included in the kit.  Simply place your hookup wire into the retainer clip in the coil and then place the coil into the coil winding arbor hole in the sounder.  {full instructions with illustrations are included in the kit’s manual} It’s possible for one person to wind the coil by themselves by using a screwdriver to turn the coil bobbin but it’s easier for two or more students to wind each coil.  One student can hold the sounder mechanism, another can turn the coil bobbin, and a third can guide the wire.  The end result, much neater coils done in less time.

The Second Problem with the Traditional Wire and Nail Experiments:

The traditional experiment of winding magnet wire around a nail and using it to make a piece of metal move is a great way to demonstrate qualitatively that electricity flowing through a conductor makes a magnetic field, however it does not leave much freedom for quantitative measurements, comparisons, or much actual scientific inquiry.  There just are not any variables that can easily be manipulated, rather just overall effects shown.  This may be fine for lower grades where you simply want to illustrate a point, but for middle and especially high school there should be more room for the scientific method and for recording data in the experiment.

Making it Quantitative:

To make my telegraph into a device that can produce measurable quantities I did two things.  Firstly, I used a sounder bar that can act as a lever when attached to a force gauge (or a force sensor from a data-logging or probeware set).  Secondly, I included two coil winding bobbins so that students can make two different coils of different measured lengths and then use a force sensor in order to determine the effect of wire length on magnetic field strength.

Teacher Tip: The coil winding bobbins can be used in two ways.  You can have the students make two different coils of different lengths (for example 20 and 40 feet of wire) and then test each one individually and record their observations on field strength (holding all other variables constant, most importantly the battery voltage powering the coil).  Alternately you can have students work in teams in a cooperative lab activity where one or two students wind a coil while another one or two students test a different coil.  In this way you can quickly move through multiple lengths in one lab period.  For example 10 feet vs. 20 feet vs. 30 feet and so on.  Using this second method a data table can be generated and then the trend graphed.

Teacher Tip: To measure the force of the electromagnetic field simply connect a force gauge to the sounder arm, engage the circuit so that the electromagnet is turned on, and while one student holds down the telegraph base another student can pull up on the force gauge until the sounder arm can be pulled away from the electromagnet.  A third student can watch the force gauge and record their observation.

Going Further (The Kit Can Do More):

I wanted my kit to have application in the home/hobby/science-fair market, and I also knew that  teachers are on a limited budget and would want the most “bang for the buck” and so I wanted to make sure that my kit could be used to teach more concepts than simple electromagnetism.  One extension was the addition of quantitative measurements as mentioned above.  Another extension is the ability to use the telegraph mechanism to teach simple circuits and switching.  To do this I made the sounder arm and the up/down stops act as an electric relay (an electromagnetically controlled switch).  Relays are useful for teaching switching concepts like those used in computers or to control electrical appliances and can be a more fun way to teach simple electric circuits along with electromagnetism.  In addition multiple kits can be connected together using some as relays to form a complete communications system {more details and instructions are in the kit’s instruction manual}

Don’t Forget the History Lesson!

Reinventing Science kits are designed to integrate history and invention and explain how real world technology works in order to make the science lessons more relevant and more exciting to students.  In our modern world of instant personal communications via cell phones, the internet, and other technologies, students may take the history for granted but in practice I’ve found that students are very fascinated to learn how communications have evolved.  It’s easy to get students into the right mind set by getting them to imagine a world where communications meant talking in person, sending mail or messages by messenger, and waiting hours, days, or even months to find out local news let alone world news.  Another link between the past and present can be made via the idea of encoding messages and “codes.”  Many students, especially older ones will have cell phones and will be used to the idea of “texting.”  Along with “texting” comes the idea of symbols and abbreviations like “LOL” for Laugh Out Loud.  It’s not too much of a stretch to explain “SOS” and how it related to something like the Titanic disaster.  You can then show Morse Code for SOS and LOL together and talk about time savings in coding messages.

Anatomy of a Real Telegraph, permission to use granted by Harris Educational

Using the Reinventing Morse Kit can be a great opportunity to partner with History or Social Studies, English, and Math teachers at your school.  The History lesson can be about the Telegraph and how it changed the world.  It has been called “The Victorian Internet.”  The English lesson can involve writing about the history of the telegraph and how it relates to text messaging today.  The Math Lesson can involve taking the data from the science experiment, constructing a data table, and then relating that to a simple linear equation and demonstrating slope.  You can even go further… measure 10 feet of wire and 30 feet of wire, and then create a graph, then use the predicted value for 15 feet and compare against observed measurements.  The possibilities are really endless!

Fun Fact: Samuel Morse’s telegraph was not the first telegraph or the first electrical telegraph.  Many systems existed in prototype stages but all were limited by technological hurdles.  One system used electrolysis of water to make bubbles in test tubes that each were labeled with a letter of the alphabet.  This system was limited by the fact that it needed 27 or more wires to convey all the letters.  Wire existed but it was expensive, imagine trying to run 27 or more wires between major cities in order to transmit letters one at a time via bubble!  Other systems used fewer wires but used a very primitive system of burying the wires underground pressed into lumber sealed with tar and pitch.  Over time water seeped into this kind of “insulation” and shorted out their system.  Morse was successful in being adopted as a technology because his system used only one wire that was placed on polls above the ground (eliminating the need for insulation or multiple wires).  The other part of his circuit used the earth as the ground.  Morse was able to use just one wire thanks to the use of Morse Code to encode each letter into a pattern of dots and dashes.  This concept of efficient encoding is still used today via the one’s and zero’s that make up binary codes, and are behind your ability to read this very blog!

As with all of my Reinventing Science kits, there is much more to each kit than what comes in the box.  I support educational users of the kits with many free resources online, a fan page and community on Face Book, and videos on YouTube.  Some of the resources available are a bibliography and reading list about telegraphs, electromagnetism, and invention, a list of science standards addressed by the kit, and other tips and tricks for using the kit.

Check out:

A Bibliography and Reading List for Reinventing Morse

Frequently Asked Questions and Troubleshooting Tips

A list of NSTA and ITEAA Standards Met by the Kit

An external Site with Telegraph History Information

An external Site with Telegraph History Information and Great Photographs

Thank you Educational Innovations for carrying Reinventing Science kits and for letting me reach out to educators via this blog.  Special thanks to teachers for taking the time to read!

If you liked this blog or the Reinventing Morse science kit, make sure to check out: Reinventing Edison: Build Your Own Light Bulb.