Back and forth with harmonic motion

Physics of the Mundane

Adam Johnston

You have two different kinds of oscillating devices.  The first is a spring, from which you may hang masses.  The other is a simple pendulum, which consists of a string with a mass hanging from one end.  (This can be in the form of a regular piece of string with a paper clip and some washers, or a yo-yo.)

Your task is simple: Find out everything there is to know about harmonic motion.  Specifically:

1. How does energy get conserved in the spring and the simple pendulum?  Describe what form the energy takes at any given moment.  You might aid your description with a sketch.

2. What variable(s) affect the period (time it takes to complete one entire cycle of swinging/bobbing), and how?  (For example, does the amount of mass hanging from a string affect the pendulum=s period?  If so, does the period increase or decrease with an increase in mass?  Is the increase or decrease proportional to the increase in mass B possibly shown with a graph?)  You should be aware of several variables, including (at least): mass, length, size of swing/bob.

You should have at your disposal the following:

C     budding researchers everywhere you look who are also tasked with this problem

C     your happy instructor

C     your text (Feynman), which has already describe the transfer of energy in other systems

C     washers (all identical mass)

C     paper clips (to hang washers from)

C     tape

C     string

C     yo-yo=s

C     springs (Slinky⁷ Junior)

C     timing devices

Note that you do not have any kind of length or mass measuring devices.  You will have to develop your own system for making these measurements.

Before you begin, you should consider how you will go about conducting an experiment that shows the dependencies of period to mass and period to length.  Within your experiments, you should be careful to only change one variable at a time B otherwise, you cannot determine which change produced a certain result.  You should also discuss how to make your collected data most reliable.  Consider how accurate you are when timing one swing of the pendulum.  Could your accuracy be improved if you recorded more than one swing of the pendulum?

Displaying your results in some creative and clear way is desirable.  Data tables and graphs would be appropriate, but feel free to come up with something else as you see fit.