Physics · 10th Grade

Active learning ideas

Simple Harmonic Motion: Springs and Pendulums

Active learning works because simple harmonic motion is counterintuitive. Students expect mass and amplitude to change the period of pendulums and springs, yet the math says they do not. Hands-on labs and structured talk let students confront their predictions with direct evidence, replacing misconceptions with durable understanding.

• Common Core State Standards
• STD.HS-PS3-1
• CCSS.HS-CED.A.2

• 20–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inquiry Circle
• 50 min · Small Groups

Inquiry Circle: Pendulum Period Lab

Groups build pendulums of varying length, mass, and amplitude using string and washers. Each group systematically varies one parameter while holding the others constant, records 10 full oscillations, and calculates period. Groups share data in a class chart, revealing which variables actually affect period and which do not.

Explain why the period of a simple pendulum is independent of its mass.

Facilitation Tip

During the Pendulum Period Lab, circulate with a stopwatch and challenge groups to measure ten consecutive periods rather than one to reduce reaction-time error.

What to look for

Provide students with the mass of a block and the spring constant of a spring. Ask them to calculate the period of oscillation for the mass-spring system. Then, ask them to calculate the frequency and verify that f = 1/T.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Period Prediction Challenge

Present a spring-mass system with a known spring constant and mass. Students individually predict the period using the formula, then pair to verify and check units. An extension question asks: what mass would you need to double the period? This forces students to reason algebraically rather than just plug in numbers.

Compare the factors that affect the period of a spring-mass system versus a pendulum.

Facilitation Tip

In the Period Prediction Challenge, give each pair only 90 seconds to write their argument before switching partners; time pressure sharpens the quality of reasoning.

What to look for

Present students with two pendulums of identical length but different masses. Ask: 'If you pull both back to the same small angle and release them simultaneously, what do you predict will happen to their periods? Explain your reasoning, considering the factors that affect a pendulum's period.'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Peer Teaching
• 25 min · Pairs

Peer Teaching: SHM Graph Analysis

Pairs receive position-vs-time data for an oscillating system and must identify amplitude, period, frequency, and angular frequency. They swap worksheets with another pair to verify answers and discuss any discrepancies, focusing on the distinction between period (time) and frequency (cycles per second).

Design an experiment to determine the spring constant of an unknown spring.

Facilitation Tip

For the SHM Graph Analysis, project one group’s graph at a time and ask the class to predict what the velocity graph will look like based on the position graph alone.

What to look for

On a slip of paper, have students draw a simple pendulum and a mass-spring system. For each, they should list the two primary physical factors that determine its period. Then, ask them to write one sentence comparing how these factors differ between the two systems.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 04

• Gallery Walk
• 30 min · Small Groups

Gallery Walk: SHM in the Real World

Post images and descriptions of real SHM systems -- clock pendulums, car suspension springs, guitar strings, seismograph needles. Groups identify the restoring force mechanism in each system and predict what physical change would increase or decrease the oscillation frequency.

Explain why the period of a simple pendulum is independent of its mass.

Facilitation Tip

During the Gallery Walk, assign each student a different color marker so you can trace which examples and explanations came from which learners.

What to look for

Provide students with the mass of a block and the spring constant of a spring. Ask them to calculate the period of oscillation for the mass-spring system. Then, ask them to calculate the frequency and verify that f = 1/T.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with a quick prediction: ask students to rank three pendulums by period before any measurement. Collect votes on the board, then let them test. The gap between prediction and data creates the strongest memory. Avoid lecturing about the small-angle approximation; instead, let students discover its limits by trying large angles. Use the phrase “characteristic frequency” repeatedly so students link the idea to real devices they know, like metronomes or playground swings.

By the end of these activities, students will confidently state that period depends only on length for a pendulum and on mass and spring constant for a spring-mass system. They will use graphs to connect position, velocity, and acceleration in SHM and cite real-world examples where these principles apply.

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Watch Out for These Misconceptions

• During Collaborative Investigation: Pendulum Period Lab, watch for students who keep the angle large to ‘get a better swing’ and then incorrectly conclude that mass changes the period.

  In the lab, hand each group a protractor and ask them to test both a small angle (10°) and a large angle (40°), then compare the periods. The data will show the small-angle approximation holds, and students will see that amplitude does not affect period within the approximation.

• During Think-Pair-Share: Period Prediction Challenge, watch for students who assume a heavier bob means a slower swing and therefore a longer period.

  After the prediction phase, have pairs use the same string length and different washers to measure period. Ask each pair to present their data and explain why mass cancels out in the equation T = 2π√(L/g).

• During Peer Teaching: SHM Graph Analysis, watch for students who use the words ‘frequency’ and ‘period’ as if they are the same.

  During the graph analysis, ask students to calculate both period and frequency from the same graph and write them side-by-side on the board. Then prompt them to convert one into the other using f = 1/T to make the reciprocal relationship explicit.

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Methods used in this brief

• Inquiry Circle
• Think-Pair-Share
• Peer Teaching
• Gallery Walk