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Pendulum
You will need:
- Three identical metal washers for each pair of students
- A metric ruler for each pair of students
- Cotton string cut in varying lengths -One length for each student pair (Variations in
string length make this activity more effective)
- Additional string
- Scissors
- A number line marked from 10 to 30 attached to the classroom wall
Give each pair of students a washer and a length of string (make sure the strings
vary in length) and have them tie the washer to the string, knotting the string
at the end. Let them practice counting pendulum swings. One student holds the
string by the knot and swings the pendulum while the other student counts the
swings. One swing is counted each time the pendulum crosses the center front of
the swinger's body. How many swings would occur in 20 seconds? Time a 20-second
interval and let the students count the swings. Allow the students to switch
roles and do the count again. If the counts are substantially different, a third
trial should be made to verify the count.
Have students form groups of four (2
pairs). Ask them to measure the string lengths from the knots to center of the
washers and record that number. They will tape the pendulums to the number line
on the wall, matching the number of swings to the number on the line. The knot
should be taped exactly on the line. The washers on the varying lengths of string
will produce a pronounced curve under the number line. What does that curve show
us? Are there other ways of presenting the relationship between the length of
string and the number of pendulum swings?
Draw a two-column table on the board
and ask each group of four to report the recorded string length and swing count
of its two pendulums. Compare and discuss the results of the pendulum swings. A
graph can provide another picture of the relation between the two variables.
Distribute graph paper to each group so they can plot the class data displayed on
the board.
What happens if we double the string length (2x) or cut it in half
(0.5x)? What shape will those lengths produce on the number line? How will they
plot on a graph? Distribute two more washers to each pair and have the students
cut 2x and 0.5x length strings. Tie and knot those pendulums and time another
series of 20-second counts with both new lengths. Let the groups tape the new
pendulums to the number line. Are the students' predictions correct? Are there
variations in the curve? How important is it to cut the 2x and 0.5x lengths
exactly? Now that we've seen a 2x length, what would a 3x length produce?
What
other variables affect pendulum behavior? Would a heavier washer give the same
number of swings in 20 seconds? What if the washer is initially dropped from a
higher or lower point? How long would the pendulum continue to swing on its own?
Test these questions as time permits.
The Teacher as Facilitator
This activity is adapted from Facilitating Systemic Change in Science and
Mathematics Education: A Toolkit for Professional Developers, a publication of
the Regional Educational Laboratories, available from NEIRL, 300 Brickstone
Square, Suite 950, Andover, MA 01810. Thanks to Diane McGowan, mathematics
instructor at James Bowie High School and David Molina, Department of Curriculum
and Instruction, the University of Texas, for their recommendations in adapting
this activity.
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