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Time that Period!

Day 1

Introduction

Students should be encouraged to discuss the definition of a cycle or periodic behavior. Examples of periodic behavior could include the movement of a pendulum or clock, the brightness of a lighthouse beam as you observe it from a fixed location, or the shape of the Moon as a function of time.

Students can get a better understanding of this concept by performing the hands-on lab described below.

Materials

Teacher	For each triad of students
roll of masking tape	2 pieces of string (one approx. 60cm, one approx. 30cm)
overhead to emphasize the points of the introduction	mass of about 1/4 to 1 kg that would serve as the pendulum bob (e.g. rubber ball, piece of clay, large key, etc.)
a few extra meter sticks to aid in measuring the lengths of the strings	wood block (recommended) or a piece of thick cardboard at least 30 cm x 30 cm
	small brass hook that would screw into the wood or cardboard
	two metric rulers
	3 sheets of graph paper
	one data table
	one metric tape measure
	stop watch or digital wrist watch with sub-second timing (you will be timing swings of a pendulum in fractions of seconds)

Procedure

(The teacher should pass the following out to each group in order for them to not only hear the procedure, but to see it as well.)

Triad decides who is:
1. Data Keeper / Reader
2. Materials Manager / Checker
3. Time Keeper / Facilitator
Materials Manager retrieves all materials listed from teacher. Reader should read all directions.
Each triad should place two chairs back to back separated by about 20 cm.
Materials manager should turn the hook into the wood/cardboard and tie the 60 cm string to the hook. S/he should also tie the 60 cm string around the mass in order that a simple pendulum is made.
A meter stick should be taped on the floor and below the pendulum, so that when the pendulum is at rest, it actually dangles over the 50 cm mark on the meter stick.
Checker and other group members should help confirm the "set-up" of the lab as seen below.
The mass of the pendulum should be gently "pulled out" by the Materials Manager to the 75 cm mark, making sure the string is taut. Now when the Time Keeper looks directly over it, he or she sees the 75 cm mark covered by the mass.
The lab should begin here (Reader--be careful to read this step carefully!).
Let time = 0 when the pendulum is released from being held over 75 cm. When the Time Keeper says go, pendulum is released and the watch started. When the pendulum reaches its maximum movement (roughly over 25 cm), someone says "stop". The measured time should be considered to be t₁. The measurement is repeated 5 times.
Show me this step!
The procedure is repeated with someone now saying "stop" the second time the pendulum reaches its maximum movement near 25 cm (this measured time should be considered to be t₂)
Show me this step!
and then again for the third time (this measured time should be considered to be t₃).
Show me this step!
You can even do this for the fourth time if the pendulum continues to reach its maximum movement!
The Data Keeper will record data for at least 3 complete swings of the pendulum (4 is, of course, better!). Each measurement should be made 5 times, and the mean determined from the 5 trials (see data table).
Again, let time = 0 when the pendulum is released from being held over 75 cm. When Time Keeper says "go", pendulum is released and the watch started. When the pendulum reaches its maximum movement, this time when it swings back over 75 cm, someone says "stop". The measured time should be considered to be t_a.
Show me this step!
The measurement is repeated 5 times. The procedure is repeated with someone now saying "stop" the second time the pendulum reaches its maximum movement near 75 cm (this measured time should be considered to be t_b)
Show me this step!
and then again for the third time (this measured time should be considered to be t_c).
Show me this step!
Once more, you can even do this for the fourth time if the pendulum continues to reach its maximum movement!
The Data Keeper will record data for at least 3 complete swings of the pendulum (4 is, of course, better!). Each measurement should be made 5 times, and the mean determined from the 5 trials (see data table).
After the data are collected and appropriately placed on the data table, it is now time to plot it.
Repeat steps 4-12, but substitute the 30 cm string for the 60 cm string.

Independent Practice

The teacher should pass out the Time that Period! worksheet to each student in order to assess individual understanding.

Day 1

Day 2

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Project Leader: Dr. Jim Lochner
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