HPP Activity 44v1
Describing what the larynx does
Exploration
Observe a slow-motion video clip of the larynx model contained in the file larynxModel.mov.
GE 1.
1. Describe the motion. Be quantitative, if you can.
Take a plastic meter stick and clamp it to a table with the end extended. Push the end down and
let it go.
GE 2.
1. Describe the motion
2. Can you make sounds with the vibrating meter stick? If so, what
characteristics of the set-up determine the sound you here?
Set up a spring so that it can oscillate in the vertical direction. Attach a mass to the end of the
spring. Make sure that the spring does not extend more than about a third of its original length.
Let the spring/mass come to rest. Now extend the mass a bit and let it go.
GE 3.
1. Describe the motion.
2. How is the motion similar to the extended meter stick and the vibrating
larynx model?
3. Are there any differences between the spring motion and the other systems?
Invention
Recall that an important part of doing physics is developing mathematical models of the
phenomena that we investigate. We will do this now for vibrating motions such as what you
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
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observed in the spring, meter stick, and larynx. Let’s start with modeling the spring, since it is
probably simplest.
All of the systems, including the spring, had some kind of repetition involved in the motion.
Motions that repeat after a set amount of time are called periodic. The period is the time
required for one complete motion. The motion associated with one period of time is called a
cycle. Sometimes we want to know how many cycles of the motion occur in a set time period,
such as one second. This number is called the frequency.
Application
GE 4.
1. Consider the oscillating mass attached to the spring. Describe one cycle of
motion.
2. Measure the period of one cycle.
3. Measure the time required for several cycles. Record both the time and the
number of cycles.
4. Calculate the frequency.
5. Can you find any relationship between the period and the frequency?
6. How do the units of period and frequency compare?
Invention
All of the systems we investigated oscillate about a certain point in space. That point defines
how the system appears when it is at rest. We call this the equilibrium point. The maximum
displacement from the equilibrium point is called the amplitude of the motion.
Application
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Consider the oscillating spring again. Hold a meter stick vertically so that you can identify the
equilibrium position. Pull the mass down, extending the spring. Note the position against the
meter stick. Now you can release the mass.
GE 5.
1. What is the amplitude initially?
2. Can you tell whether the amplitude changes over time?
Open up one of the vibrating meter stick videos in VideoPoint. Observe the end of the meter
stick move.
GE 6.
1. What is the period of the meter stick vibration? You will need to use the
camera frame rate to help answer this question.
2. Measure the amplitude of the end point at the beginning of the oscillating
motion.
3. Compare your amplitude measurement with other groups and resolve any
differences. Make sure you are using the right definition for the amplitude.
Invention
The simplest type of oscillating motion is called simple harmonic motion. The displacement
away from equilibrium of an object undergoing simple harmonic motion is described by a
sinusoidal function. The general form for the displacement as a function of time of an object
undergoing simple harmonic motion is
x  A cos( t   )
where
x is the displacement from equilibrium.
A is the amplitude.
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(1)
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 is the angular frequency.
is the phase.
The angular frequency, , is determined from the regular frequency, f, by the relationship
  2 f
(2)
The phase, , is determined by the object’s displacement at t = 0, x0.
 x0 
(3)

 A
where the positive or negative sign must be determined by looking at the direction of motion at
t=0.
   cos 1 
Application
We will obtain some quantitative data for the oscillating spring and see if the simple
mathematical model introduced above can describe it.




Set up the spring/mass system vertically, as
shown in the figure.
Let the hanging mass come to rest, so that
you can note the equilibrium position.
Place the ultrasonic motion detector
underneath the hanging mass.
Place a wire cage over the motion detector,
if available, otherwise, make sure the mass
is securely fastened to the spring.
GE 7.
1. The motion detector will indicate the distance of an object from the
detector. Draw an appropriate coordinate axis for measuring the hanging mass
location using the motion detector.
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 2010 The Humanized Physics Project
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2. Measure the equilibrium position of the hanging mass in this coordinate
system. This means measure the distance from the motion detector to the
hanging mass. Record here:
3. Record the mass of the hanging object:
4. Practice collecting position versus time data for the oscillating mass using
Data Studio. When you get at about three cycles of good data save it and
paste a graph here:
5. Do the oscillations show significant damping over the time period
considered above? Give a quantitative estimate for any change noticed.
6. What is the approximate amplitude of the oscillation, over the time period
considered?
7. What is the period of the oscillation?
We need to see if the simple harmonic motion mathematical model works well for this data.



Copy your position versus time data over to the spreadsheet program.
Set up a column that contains the position at each time measured on an axis, which has an
origin at the equilibrium point.
Try to fit the data using equation (1). Set up a “Theory” column and find the amplitude,
angular frequency, and phase that give the best agreement between theory and experiment.
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 2010 The Humanized Physics Project
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GE 8.
1. Write down the final equation that you think best fits the data.
2. Paste a spreadsheet graph that shows the data as points and the theory as a
continuous line.
3. Do you think the mass attached to the spring undergoes simple harmonic
motion over the time period considered?
Application
We will check whether the end of the vibrating meter stick undergoes simple harmonic motion.
Open up one of the vibrating meter stick videos in VideoPoint, either file ruler30cm.mov or
ruler40cm.move.
GE 9.
1. What data must you collect in order to check whether the motion is simple
harmonic?
2. Discuss how you will collect position measurements. Will you need to
transform the measurements in some fashion before trying to fit the data to
equation (1)?
3. Make an appropriate spreadsheet showing your data and theoretical fit.
Paste the spreadsheet table here.
4. Make any appropriate graphs for comparing theory with experimental data
and put them here.
5. Do you think the end of the vibrating meter stick undergoes simple
harmonic motion?
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 2010 The Humanized Physics Project
HPP Activity 44v1
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Exploration
Vibrating systems such as the vocal folds of the larynx or an object attached to a spring behave in
similar ways. We will explore why systems that look so different can be very similar in
behavior. Since the spring system is easy to manipulate in the lab, we will continue investigating
it as one of the simplest vibrating systems.
Set the spring up vertically. Do not attach the hanging mass yet.
GE 10.
1. Pull on the end of the spring with your hand. While you are exerting a force
on the spring with your hand, what is the spring doing?
2. Where is the spring trying to pull your hand?
3. Try compressing the spring with your hand. Where is the spring trying to
push or pull your hand?
4. Devise a rule for the direction of the force that a spring exerts on an object.
5. Pull the spring down below its equilibrium point again. What happens to
the pull force that your hand exerts on the spring as you extend it further?
6. Make a hypothesis about the relationship between the force a spring exerts
on an object and the object’s displacement from equilibrium.
Invention
Systems undergoing vibrations have an equilibrium configuration such that under certain
circumstances, if the system starts in that configuration it will remain in that configuration. For
example, the spring has a length for which it is unextended and uncompressed. If it starts at that
length and is not given any initial velocity then it stays at that length.
When a vibrating system departs from its equilibrium configuration one part of the system will
exert a restoring force, which tends to return the system to its equilibrium configuration. In the
case of an object attached to a spring, when the spring is extended beyond its equilibrium length,
it exerts a force on the object that tends to pull it back to the equilibrium position. The spring
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exerts a restoring force. The direction of such a force is always back towards the equilibrium
position.
In the simplest case the restoring force is proportional to the displacement from equilibrium.
F  kx
(4)
This force law is called Hooke’s Law. The constant of proportionality, k, is called the spring
constant. Note that x is measured from the equilibrium point, and can be positive or negative,
depending on which side of the equilibrium the object is located.
Application
Does your spring obey Hooke’s law?
GE 11.
1. What data must you collect in order to answer this question?
2. How might you measure the force that the spring exerts on a hanging object
attached to it?
3. Create a proposed experiment for determining whether the spring obeys
Hooke’s Law. Have it approved by the instructor, and then describe it here.
4. Record an appropriate data table here, with data in it.
5. Paste any appropriate graph here.
6. Does your data suggest that the spring obeys Hooke’s Law?
7. Estimate the spring constant from your data. Include an uncertainty
estimate.
8. What are the units of the spring constant?
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9. Is there any relationship between the spring constant and the vibration
frequency for an object attached to a spring? You might use data from other
groups with different springs to help answer this question.
Application
Think about the vocal folds of the larynx, or the simple mechanical model we constructed of
them.
GE 12.
1. Do the vocal folds have an equilibrium configuration?
2. Is the idea of a restoring force applicable to the vocal folds?
3. Does Hooke’s law provide a good description for the latex strips in our
larynx model? Investigate this problem with the XRAYS strategy. Explore
the strip behavior and compare it to a spring.
4. Record relevant data for comparing the force and displacement of the strip.
Draw an appropriate diagram.
5. Try to apply an appropriate theoretical equation to describe your data.
Describe here your plan for applying the theoretical equation.
6. Execute your plan for yielding a solution. If a spreadsheet is used for
calculations, paste it here.
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7. Scrutinize your theoretical calculation. Does it make sense?
8. Assuming your calculation appears correct, then comment on how well
Hooke’s law describes the latex strip behavior.
Activity Guide
 2010 The Humanized Physics Project