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
|
|
|
|
|
|
|
|
|