Lab
Introductory Simple Pendulums
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Background:
At the turn of the century 400 years ago, Galileo was completing his examination of the study of motion and had discovered a profound relationship of a pendulum and its period (the time to complete a swing). Before Galileo, no one had every noticed the regularity of this common phenomenon. His discovers allowed time keeping to be done to accuracy 1000 times greater than in the past.
The myth is that he discovered this relationship while watching an urn filled with burning incense swing at the end of a chain during a church service. It is suggested that he measured the swing with the beating of his heart, but I like to think that it was the melody within his head, that lead him to discover that the period of a pendulum is constant.
Equipment:
meter stick
fishing line
hooked mass
protractor
Procedure
Setup a pendulum with the hooked mass suspended from the end of a string.
Record the values stamped on the mass below.
Set the length of the pendulum to approximate length, indicated in the data table below, by winding or unwinding the string about the support. NOTE: one winding equals approximately 5 cm.
Measure your actual length to the closest tenth of a centimeter and record in the table below; make sure to measure to the vertical center of the hanging mass, or bob.
Swing the pendulum from an angle of approximately 10 degrees.
Record the time to make 10 complete vibrations. Repeat three times for each length.
The
period of a pendulum
is defined as the time (in seconds) required for one complete vibration. To calculate its value in the data table below, you will take the average of your three times for 10 vibrations and divide by the number of vibrations in each trial, 10.
The
frequency of a pendulum
is defined as the number of vibrations occuring each second. It is measured in hertz, hz. One hertz means one vibration per second. To calculate its value in the data table below, you will divide the number of vibrations in each trial, 10, by the average of your three times. Frequency is the multiplicative inverse, or reciprocal, of period.
Refer to the following information for the next four questions.
Data Table
Approximate Length (cm)
Actual Length (cm)
Trial #1
time for 10 vib
(sec)
Trial #2
time for 10 vib
(sec)
Trial #3
time for 10 vib
(sec)
Average time for 10 vib
(sec)
Average Period (sec)
Average Frequency (hz)
15
25
35
45
55
65
75
85
95
What was the mass of your pendulum's bob in grams?
Which of the following is the independent variable in this experiment?
frequency, length, mass, period, time
Which of the following is the a control variable(s) in this experiment?
frequency, length, mass, period, time
Why were you asked to allow the pendulum to swing ten times, rather than just once?
Once your table is complete, open the EXCEL workbook
1-pendulum
on the file system and fill out the required information on each worksheet. Remember to rename the file as
Pendulum_LastnameLastname.xls
before placing any of your group's information in the file.
Refer to the following information for the next five questions.
These questions refer to the graph on Sheet 1 of your EXCEL workbook.
What is the title of your EXCEL workbook?
What is the coefficient of restitution, R
^{2}
, for your graph?
What is the exponent of x on the equation of your graph?
What is the shape of this graph?
Does the period increase, decrease or remain unchanged as the pendulum's length increases
Refer to the following information for the next three questions.
These questions refer to the graph on Sheet 2 of your EXCEL workbook.
What is the shape of this graph?
State the equation of your graph using the correct variables for each axis: T
^{2}
for y, and L for x.
Using the equation for your graph extrapolate the time required for a 120-cm pendulum to make ten vibrations. NOTE: We will not be examining the slope of this graph until the beginning of next semester when we discuss the acceleration due to gravity.
Refer to the following information for the next three questions.
These questions refer to the graph on Sheet 3 of your EXCEL workbook.
What is the shape of this graph?
Is the frequency of a pendulum directly or inversely proportional to the square root of its length?
Based upon the graphical patterns in these introductory labs, how could the data shown on this third graph be rectified to create a straight line?
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William A. Hilburn
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