Pendulums #01

(grades 8-12)
Soft-bound, 56 page book, 20 reproducible task cards, full teaching notes.

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A washer swings on a thread, sweeping the face of a cereal box. This box is covered with a grid that measures length and amplitude. It is, in short, a classically simple TOPS learning system. Using a stopwatch and calculator, your students will graph length vs frequency into a beautiful curve; they'll stand this curve on its head by plotting the period, then straighten it back out by squaring the period. This straight line leads directly to a simple pendulum equation with powerful applications. Math teachers, don’t miss this one!

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Table of Contents for #01 Pendulums:

Preparation and Support

A TOPS Model for Effective Science Teaching • Getting Ready • Gathering Materials • Sequencing Task Cards • Gaining a Whole Perspective• Long Range Objectives • Review/Test Questions

Activities and Lesson Notes

  1. 1. Pendulum Box
  2. 2. Frequency
  3. 3. Length vs. Frequency
  4. 4. Period
  5. 5. Length vs. Period
  6. 6. Amplitude and Bob Weight
  7. 7. Boinggg!
  8. 8. Extrapolate
  9. 9. Square It
  10. 10. Pendulum Equation
  11. 11. Chain Links (1)
  12. 12. Chain Links (2)
  13. 13. Square Roots
  14. 14. Roll and Rock
  15. 15. Energy Bridge

  17. 16. Two-Pivot Pendulum
  18. 17. Conservation of Energy
  19. 18. Energy Curve
  20. 19. In Orbit
  21. 20. It's Refreshing

Supplementary Pages

pendulum grid • graph paper • metric ruler • disk with holes


Complete Master List for #01 Pendulums:

Key: (1st/2nd/3rd) denote needed quantities: (1st) enough for 1 student doing all activities; (2nd) enough for 30 students working in self-paced pairs; (3rd) enough for 30 students working in pairs on the same lesson. Starred* items may be purchased below.

  1. 1/10/10: cereal boxes (two pound Grape Nuts boxes are ideal)
  2. 2/20/20: cups gravel (sand or soil)
  3. * 1/5/5: rolls of masking tape
  4. 1/10/10: scissors
  5. * 1/2/2: spools thread
  6. * 2/20/20: washers sized to fit quarter-inch bolts
  7. * 1/2/3: boxes of paper clips of uniform size
  8. 1/1/1: wall clock with second hand (wrist watches)
  9. 1/1/010: stopwatches
  10. 1/10/10: hand calculators

  11. * 1/1/1: roll thin, bare iron wire, about 30 or 32 gauge
  12. 1/5/10: meter sticks
  13. 1/2/5: wire cutters
  14. 1/4/10: batteries, size-D, dead or alive
  15. * 1/4/10: clothespins
  16. 1/10/10: index cards (any straight edge)
  17. * 1/20/20: straws
  18. * 4/30/40: straight pins
  19. 1/10/10: 4 1/2 inch plastic lids from margarine tubs or coffee tins
  20. 1/2/5: paper punches
  21. 1/1/1: a working video screen

Convenient Shopping:


wooden, spring-action

These are handy lab items to keep in stock. We use them as bulb holders, tongs, clips, and more.

Paper Clips

size #1, steel, box of 100

Paper clips have 1001 uses in TOPS experiments, and science in general. Feel free to use paper clips you already have, but be aware that different brands come in different sizes and weights. In experiments where uniformity is important, don't mix brands.

Straight Pins

steel, one and 1/16 inch long

Used in many TOPS experiments. Sometimes required for their magnetic properties. Don't purchase aluminum straight pins by mistake.

Straws - straight

plastic, thin

Any length straw, between 0.20 and 0.25 inches in diameter is suitable. Grocery stores generally carry straws with flexible "elbows." You can use those if you cut off the bendable section before using.

Tape - masking

3/4 inch x 55 yd roll

A handy science supply used in most TOPS modules.


light duty, 25 yd spool

Just plain old thread. Used in many TOPS titles, especially in Pendulums #34.

Washers - small

7/8 inch flat washer with 3/8 inch hole

Used in many TOPS labs. Item #1290 (medium tubing) used in #16 Pressure fits through these smaller washers.

Wire - 32 gauge iron

bare wire

A specialty item used in #01 Pendulums.

Teaching Tips for #01 Pendulums:

We encourage improvisation - it's one of the main goals of our hands-on approach! You and your students might invent a simpler, sturdier or more accurate system; might ask a better question; might design a better extension. Hooray for ingenuity! When this occurs, we'd love to hear about it and share it with other educators. Please send ideas and photos to

Lesson by Lesson Objectives for #01 Pendulums:

  1. Lesson 1: To construct a cereal-box pendulum support with a length and amplitude background grid for use in activities throughout this module.
  2. Lesson 2: To find the frequency of a pendulum in cycles per minute for various lengths. To summarize how the frequency of a pendulum varies with length.
  3. Lesson 3: To convert pendulum frequencies from cycles per minute to cycles per second, or hertz units. To graph how the frequency of a pendulum varies with length.
  4. Lesson 4: To find the period of a pendulum in seconds per cycle for various lengths. To summarize how the period of a pendulum varies with length.
  5. Lesson 5: To understand the inverse relationship between period and frequency, both mathematically and graphically.
  6. Lesson 6: To evaluate the relative effects of length, amplitude and bob weight on the period of a pendulum.
  7. Lesson 7: To apply concepts and skills in the study of washer pendulums to a new oscillating system -- a spring pendulum.
  8. Lesson 8: To extrapolate the graph line of length vs. period to longer lengths. To evaluate the accuracy of this prediction.
  9. Lesson 9: To graph how the length of a pendulum varies with the square of its period. To observe that the ratio of these variables yields a constant number.
  10. Lesson 10: To derive an equation that relates the length of a pendulum to its period. To apply this equation in a predictive way and confirm that it is valid.
  11. Lesson 11: To graph how the period of a paper-clip chain changes with length. To compare its graph line with a thread and washer pendulum.
  12. Lesson 12: To apply concepts and skills learned with thread pendulums to paper clip pendulums. To develop an equation relating the period of a paper clip chain to the number of clips it contains.
  13. Lesson 13: To experimentally calculate square roots using pendulum variables.
  14. Lesson 14: To study how pendulums receive energy pulses at simple multiples of their own natural frequency.
  15. Lesson 15: To transfer energy between pendulums of equal and unequal length. To account for observed differences in terms of frequency and phase.
  16. Lesson 16: To examine a pendulum system with two distinct pivot points. To develop an equation for calculating its period.
  17. Lesson 17: To study energy transformations in a swinging pendulum. To understand that energy in the bob is always conserved.
  18. Lesson 18: To graphically analyze how energy in a pendulum system changes forms.
  19. Lesson 19: To graph the energy of a washer that revolves full circle. To compare this system to a low-amplitude pendulum.
  20. Lesson 20: To calculate the refresh rate of a video screen in hertz units.

National Science Education Standards (NRC 1996) for #01 Pendulums:

TEACHING Standards

These 20 Task Cards promote excellence in science teaching by these NSES criteria:
Teachers of science...
A: ...plan an inquiry-based science program. (p. 30)
B: and facilitate learning. (p. 32)
C: ...engage in ongoing assessment of their teaching and of student learning. (p. 37)
D: and manage learning environments that provide students with the time, space, and resources needed for learning science. (p. 43)

CONTENT Standards

These 20 Task Cards contain fundamental content as defined by these NSES guidelines (p. 109).
• Represent a central event or phenomenon in the natural world.
• Represent a central scientific idea and organizing principle.
• Have rich explanatory power.
• Guide fruitful investigations.
• Apply to situations and contexts common to everyday experiences.
• Can be linked to meaningful learning experiences.
• Are developmentally appropriate for students at the grade level specified.

Unifying Concepts and Processes

NSES Framework: Systems, order, and organization • Evidence, models and explanation • Constancy, change, and measurement • Evolution and equilibrium • Form and function
Core Concepts/Processes: Explore change, constancy, measurement and pattern in pendulum systems. • Study frequency variables that really matter (length); that don't matter (bob weight); that matter a little (amplitude).

Science as Inquiry (content standard A)

NSES Framework: Identify questions that can be answered through scientific investigations. • Design and conduct a scientific investigation. • Use appropriate tools and techniques to gather, analyze, and interpret data. • Develop descriptions, explanations, predictions, and models using evidence. • Think critically and logically to connect evidence and explanations. • Recognize and analyze alternative explanations and predictions. • Communicate scientific procedures and explanations. • Use mathematics in all aspects of scientific inquiry.
Core Inquiries: Time Pendulums • Measure Lengths • Record Data • Graph Variables • Predict Frequency

Physical Science (content standard B)

NSES Framework: Motions and forces • Transfer of energy • Conservation of energy Core Content: Explore how length, amplitude and bob weight affect pendulum frequencies and periods. • Collect and graph data. • Examine energy transfers.

Science and Technology (content standard E)

NSES Framework: Abilities of technological design • Understanding about science and technology Core Content: Study levers, pulleys, inclined planes, wheels and axles, and gears.