The following is a sample of what a research report could look like.  This was written using real data.  While it might resemble a study that you are doing, you should be sure to produce your own data and your own descriptions and conclusions.  This is just an example of the depth that is expected for this project.  (Note: The author of this piece is a little bit more wordy than most authors.  She gets that from her mother.)

## The Swinging Bowling Ball Pendulum

Anna Johnston

April 11, 2001

Research Project
Introduction to Physics (PHSX 1010)

### Introduction: The boring life of a physicist's daughter

Back when I was but a young child, my Daddy would take me aside and try to convince me that his life's aspirations are worthwhile.  Uncoiling the string of a yo-yo and letting it swing back and forth as a pendulum, he would try to lecture.  "Look Anna," he would say, "this yo-yo swings back and forth in perfect symmetry, always rising back to the same height on both sides, and always swinging with the same velocity at the bottom of its path, showing the beauty and simplicity of energy conservation . . . "  Strangely, I would fall asleep during my father's physics lectures; but now that I have grown older (15-months-old) and wiser (I can imitate an elephant!) I can appreciate the wonders of the natural universe.

It turns out that the yo-yo that swings back and forth really is interesting after all.  At first, it seemed like a pretty stupid idea for a research project.  Swinging-back-and-forth motion isn't exactly my idea of "thrilling."  Lately, though, I've been wondering how I could make my swing go back and forth faster.  As I began to ponder a modification to the original Fisher Price design, it occurred to me that my swing is a pendulum, just like the yo-yo that swings to and fro.  When Daddy wears a tie, it swings back and forth with each step -- it's a pendulum too!  There aren't too many other pendulums in my life, since my toys all have very short pull strings because apparently it is all too easy for me to strangle myself on these kinds of things.  Still, we can see pendulums in clocks, on key chains, and as hanging chandeliers.  If we just look a little closer, I would bet that we could see them all around us.

As I began to get more interested in pendulum motion, I started to devise a research plan.  I wanted to see what determined the motion of a pendulum.  Specifically, I wanted to see how a simple pendulum's length, mass, and swing-width (sometimes called "amplitude") affect its period (the time it takes to swing back and forth once).  Originally, I proposed using a "bowling ball pendulum" like the one in the physics lecture hall at Weber State, but I decided that this would be too hard to use in the comfort of my own home.  I determined that, since the natural universe is very consistent, I could use a smaller version of this pendulum and get similar results.  Not only would my results inform my knowledge of the bowling ball pendulum, but it would also help me to understand how to make my swing go faster.  What follows are my descriptions of my research and its results.

### Methods: Poking at the natural world

My pendulum materials consisted of a tripod, some string, some wood blocks, and some paper clips.  In addition, I had a stopwatch and a meter stick to make measurements.  Except for the wood blocks (which belong to me), these items were stolen from the physics department by my Daddy.  The accompanying photos show some of the equipment.

As you can see from the photos, I spent much of my time wandering around the house with a stopwatch hanging around my neck.  The stopwatch was so long on my body that I would sometimes trip on it, start crying, and have to wrestle with the cord to get myself back on my feet.  Daddy says that he sometimes has the same problems.

I also spent a fair amount of time placing different amounts of mass on a string of varying length, and swinging the pendulum back and forth from different amplitudes or widths.  (In the data to follow, the distance that I pull the block back is referred to as a swing "size" or "width;" but this is referred to as "amplitude" in many physics books.)  I would time how long it took for the pendulum to swing back and forth (one "period of oscillation") five times.  I figured that I would be able to measure the time for 5 swings more accurately than 1 swing, since I'm still working on my hand/eye coordination and my reactions aren't as good as they will be a few years from now.  Since each swing of the pendulum was consistently the same, I assumed that this would not be a problem.

I was able to measure distances (both length and swing width) in centimeters (cm).  This is a standard scientific unit of measurement.  For mass, however, I made up my own units, defined by the square blocks (and half-blocks) that I had on my toy shelf.  Someday, when I'm old enough to work a scale, I may be able to convert "blocks" to "kilograms" or some other standard unit of mass.

In this study, I wanted to make sure that I only varied one thing at a time.  (Otherwise, I wouldn't be able to make any really firm conclusions.)  So, I varied the mass of the pendulum while keeping the swing width the same (6 cm) and the length the same (60 cm).  Next, I varied the length of the pendulum, keeping the mass the same (2 blocks) and the swing width the same (6 cm).  Finally, I varied the swing width while keeping the length constant (40 cm) and the mass constant (2 blocks).  For each variation, I recorded 3 times.  This way I could make sure that I was getting reliable results.  Samanda the Panda (my friend) helped me collect data accurately.  She also babysat while Mommy and Daddy went out for pie at Denny's.

All of my data were collected and written down in a notebook.  Samanda the Panda helped me write everything down on the paper.

### Results: Uncovering the natural world

Because I collected such great data, this section is comprised mostly of graphs and data tables.  These represent each of the 3 variations: mass, length, and width.  In each data table and in each graph, you will notice that I have multiple measurements of time for each measurement of mass, length, or width.  I could have averaged these values, but I wanted to color more points on the graph.  The graphs are a nice way to show us all the data at the same time, and essentially allow us to see the averages visually.

(For each of the data sets below, click on the small graphs to show the full-size version.)

We begin with the data representing the changing mass:

 mass (blocks) time (5 swings) (seconds) 0.5 0.5 0.5 1.0 1.0 1.0 2.0 2.0 2.0 3.0 3.0 3.0 4.0 4.0 4.0 7.87 8.01 7.99 8.19 8.05 8.02 8.00 8.12 8.00 8.09 7.95 7.93 8.12 8.09 8.09

The above table and graph (click on the graph to see the full size version) show what happens when I changed the mass of the blocks. I was surprised to see that, for the most part, changing the mass did not do anything noticeable to the time it took for the pendulum to swing back and forth.  While all of my values for time are different from one another, these differences are only varying by a few fractions of a second.  This is simply accounted for by the fact that Samanda and I are only panda and human respectively, and we react a little differently each time we press the stopwatch.

The next set of data represents the variation in the length of the pendulum:

 length (cm) time (5 swings) (seconds) 20.0 20.0 20.0 30.0 30.0 30.0 40.0 40.0 40.0 50.0 50.0 50.0 4.64 4.83 4.70 5.60 5.71 5.85 6.52 6.59 6.66 6.92 6.99 6.99

These data (click on the graph to see the full size version) show that, unlike the mass, a change in length will affect the period of a swing.  This is exciting to see -- I was beginning to think that physics was boring!  The time increases as the length increases.  But, by looking closely at the graph and the data, I can see that the relationship between length and time is a little tricky.  They both increase, but the time does not increase as much for large lengths.  In other words, the graph makes a curve (rather than a straight line) that gets less and less steep as the length measurements increase.  There is probably some kind of mathematical function that could be figured out here, but I am going to wait until I've entered kindergarten before I attempt to figure that part out.

Finally, we can look at how the width of the pendulum's swing affects the time of the swing:

 width (cm) time (5 swings) (seconds) 3.0 3.0 3.0 6.0 6.0 6.0 9.0 9.0 9.0 12.0 12.0 12.0 6.66 6.59 6.63 6.49 6.67 6.54 6.53 6.57 6.57 6.66 6.70 6.64

This table and graph (click on the graph to see the full size version) show that the swing width does not affect the time of the swing.  This is a little bit confusing to me, since a bigger swing (in my mind) would seem to need to take longer to go back and forth.  However, as I watched the swinging take place, I noticed that the bigger swings (like the 12 cm width) would travel with higher speeds than the smaller swings.  So, even though the big swings had to move farther, they also moved faster.  Therefore, they took the same amount of time as the small swings.  It's amazing how pendulums have figured this out!

### Discussion and conclusion: Explaining the natural world

After taking all this data, I was really tired, and it was almost my bedtime (7:00 PM).  All of the excitement of doing physics research really takes a lot of energy!

I am happy to report that I learned much about physics in general by doing this research.  More specifically, I learned about how pendulums work and how they might apply to me.  To summarize, I found that changing the mass or width of a simple pendulum does not affect its swing time; but changing the length of the pendulum does affect the swing time.  An increase in length increases the swing time, but the amount of increase is not a constant amount.

I can apply these features of a pendulum to my swing outside.  From my research, I can see that even when I grow up and get bigger (more mass), I will still swing back and forth at the same rate.  Also, I will have the same time to swing back and forth no matter how far my Daddy pushes me; but this means that I will have to travel faster to make up the big distances of a big swing (if I'm going to travel with the same swing period, regardless of swing size).  Finally, I see that I can change the nature of my swing if I make the swing's ropes longer or shorter.  I think that I would like a very long swing so that I could spend a lot of time traveling back and forth.

I think that when I do this research again, I will collect more data that compares the pendulum length to the swing time.  I would like to look at the details of this relationship, because I still have some questions.  First, if the pendulum length is very very short, how fast will the period get?  Also, as the length gets very very very very large, how slow will the period get?  Is there a limit to how long a swing can take?  Finally, what exactly is the mathematical relationship between length and period?  Do they cover this in kindergarten?

Even though I was not very excited about this research at first, I'm glad that my Daddy forced me to do it.  I would like to do some more physics research in the future (maybe tomorrow), either in blowing soap bubbles or in quantum electrodynamics (QED).  I've learned that physics isn't just a bunch of boring lectures and numbers like when my Daddy drones on and on and on.  Instead, physics (and science in general) is a way of understanding and making sense of the world.  It's nice to know that this kind of work can be done to make the world a less confusing place.

### Acknowledgments

I would like to thank Samanda (the Panda) for being my research assistant.  Also, Mommy supported me with a snack that Sam and I shared.  Finally, Tycho (the dog) stayed out of my way and didn't chew on the stopwatch too much.