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.

• 10th Grade
• Physics
• 4 activities
• 20 min–50 min

Learning Objectives

1. Calculate the period and frequency of a mass-spring system given the spring constant and mass.
2. Compare the factors influencing the period of a simple pendulum (length, gravity) versus a mass-spring system (mass, spring constant).
3. Design and conduct an experiment to determine the spring constant of an unknown spring using Hooke's Law.
4. Explain why the mass of a simple pendulum does not affect its period for small amplitudes.
5. Analyze the mathematical relationship between displacement, velocity, and acceleration in simple harmonic motion.

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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).

Prepare & details

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.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

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.

Prepare & details

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.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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).

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After the Gallery Walk, give students a 5-question exit quiz: two questions ask for period and frequency calculations for a spring-mass system using given m and k values, and three questions ask students to interpret real-world SHM examples they saw on the posters.

Discussion Prompt

During Think-Pair-Share: Period Prediction Challenge, ask each pair to write their prediction and reasoning on a whiteboard. Circulate and look for whether they correctly identified length as the only factor for pendulums and mass and k for springs.

Exit Ticket

After Collaborative Investigation: Pendulum Period Lab, have students complete an exit ticket drawing a pendulum and a spring-mass system, labeling the two primary factors that determine each system’s period and writing one sentence comparing those factors between the two systems.

Extensions & Scaffolding

• Challenge early finishers to design a pendulum that ticks at exactly 1.00 Hz and then test it with a smartphone app.
• For struggling students, provide a data table with missing values for period and length; ask them to fill in the pattern.
• Use extra time for a discrepant event: hang a spring vertically with a mass and ask students to explain why the equilibrium position shifts before they begin oscillation measurements.

Key Vocabulary

Simple Harmonic Motion (SHM)	A type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction.
Period (T)	The time it takes for one complete cycle of oscillation in a system, measured in seconds.
Frequency (f)	The number of complete cycles of oscillation that occur per unit of time, typically measured in Hertz (Hz).
Spring Constant (k)	A measure of the stiffness of a spring; a higher spring constant indicates a stiffer spring that requires more force to stretch or compress.
Hooke's Law	A law stating that the force needed to extend or compress a spring by some amount is proportional to that distance (F = -kx).