PEP 201 Lab -- Pendulum
PEP 201 Lab
Pendulum
Department of Physics
Stevens Institute of Technology
a
PEP 201 Lab -- Pendulum
d 2
 MgX sin 
Equation of Motion: I
2
dt
The hole
Lrod
When  is small, we have:
Hbob
sin   
d 2 MgX
The equation reduce to:


2
dt
I
This is the second order differential
equation, solving this equation, we obtain
T  2
Measure
Mrod
Mbob
where
I
MgX
MgX  M rod gX rod  M bob gX bob
I  I rod  I bob
M rod Lrod 2

 M rod X rod 2  M bob X bob 2
12
PEP 201 Lab -- Pendulum
1. Calculate the theoretical period
In order to calculate the theoretical value of the period, we need to measure
the following five values:
Mrod, Mbob, Lrod, Hbob, a
Then, subsititute all of those value to the equation.
T  2
where
I
MgX
MgX  M rod gX rod  M bob gX bob
M rod Lrod 2
I  I rod  I bob 
 M rod X rod 2  M bob X bob 2
12
L
H
X rod  rod  a X bob  Lrod  a  bob
2
2
We can use Excel file to calculate this value directly.
See Excel file attached.
PEP 201 Lab -- Pendulum
A. Measure the period in the experiment
1. Measure five values Mrod, Mbob, Lrod, Hbob, a
2. Install all the equipment as the “sample” shown to you.
3. Turn the power, Open the “Data Studio”. Add a Rotary motion sensor, set:
sample rate=500Hz, divisions=1440, measure the angular position, open a
“graph” to observe the figure.
4. Use the “smart tool” to measure the time interval and record the results
both on the blue book and on your laptop.
5. You may calculate the AVERAGE and the STDEV yourself or just use the
EXCEL file to get it directly.
6. Compare the experiment result to the theoretical value.
Section A is finished; the following things must be recorded: original data
and one graph of the oscillating pendulum.
PEP 201 Lab -- Pendulum
PEP 201 Lab -- Pendulum
B. Measure the damping constant
1. Set the RMS correctly. Sample rate=500, division=1440 measure the angular
position. Then place a damping device on the top of the RMS.
2. Open a graph, observe the damping process.
3. Measure each peak value and the time point of this peak (using smart tool) to
calculate the damping constant. The data must be recorded both on the blue
book and on your laptop.
4. Calculate the damping constant. You can design a program yourself or just
input the data into the sample EXCEL file to get it directly.
5. Let the damping device a little near to the disk repeat the process above.
Section B is finished. Original data and two graphs of the damping process
are needed.
PEP 201 Lab -- Pendulum
Equation
b  2m ln yi 1 yi (ti 1  ti )
For details of the
derivation, see the
menu
PEP 201 Lab -- Pendulum
C. Observe the phenomenon of chaos
In this section, the only thing you need to do is just observe and write down what
you have observed in you experiment report. (The graph will be send to you by TA)
Chaos theory is a field of study in mathematics, with applications in several
disciplines including physics, engineering, economics, biology, and philosophy.
Chaos theory studies the behavior of dynamical systems that are highly sensitive to
initial conditions, an effect which is popularly referred to as the butterfly effect.
PEP 201 Lab -- Pendulum
PEP 201 Lab -- Pendulum
Week 2:
Observe the coupled pendulums
1. Set two RMS correctly. Set sample rate=100Hz, division=1440, measure the
angular velocity.
2. Displace one pendulum and make the other one still stand, observe the graph.
3. Displace both two pendulums to the same altitude, observe the graph.
4. Change the position of one bob on the rod to change its period, then displace one
pendulum and leave the other one still stand. Observe the graph.
5. Save all the graphs you observed. (Do not forget!!!)
All the graphs (3 in total) must be saved.
2. Complete the experiment report
There will be a sample report. However it is just a sample, you can write your report in your
own style. In general, except the introduction and conclusion, the experiment report should
include:
•the theoretical study of the period of the pendulum.
•the data and graph in the experiment “measure the period”.
•the data and graph in the experiment “measure the damping constant”.
•the data and graph in the experiment “coupled pendulum”.
•the graph of “chaos”.
You can also write something in each experiment, such as “what you have learned from the
experiment”, “analyze some problems occurred in the experiment”…
Original data should be included.
Finally, there are some questions for you to answer: (optional)
1. Why the rotational inertia of the bob about its mass center can be neglected during the
calculation?
Hint:
2. Discuss the energy transfer between the two coupled pendulums in the experiment. (Based
on the graphs you got from the experiment)