Simple Harmonic Motion: Springs and Pendulums

Active learning lets students confront misconceptions hands-on by testing period dependencies directly, rather than relying on passive exposure. When students collect their own data on mass, length, and amplitude, they internalize the conditions for SHM instead of memorizing formulas.

• 12th Grade
• Physics
• 3 activities
• 20 min–65 min

Learning Objectives

1. Calculate the period and frequency of a mass-spring system given its mass and spring constant.
2. Analyze the relationship between the length of a simple pendulum and its period for small angular displacements.
3. Compare and contrast the factors affecting the period of a mass-spring system versus a simple pendulum.
4. Identify the conditions under which a system exhibits simple harmonic motion, distinguishing it from other types of oscillation.
5. Predict the effect of changing mass, spring constant, length, or gravitational acceleration on the period of SHM systems.

Inquiry Circle

⏱ 65 min·Small Groups

Inquiry Circle: What Affects Period?

Groups systematically vary one factor at a time (mass on spring, spring constant, pendulum length, pendulum mass, amplitude) while measuring period with a stopwatch or motion sensor. Students record results in a structured data table and identify which variables affect period and which do not, supporting claims with evidence from their own measurements.

Prepare & details

Explain the conditions necessary for an object to undergo simple harmonic motion.

Facilitation Tip: During Collaborative Investigation: What Affects Period?, circulate with a timer visible on your phone to coach groups on consistent counting methods for small and large swings.

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: The Pendulum Clock Problem

Ask students to predict how a grandfather clock with a 1-meter pendulum should be adjusted if it runs slow. Pairs work through the period formula to determine the required length change, then discuss what would happen on the Moon. Whole-class sharing connects the formula to real-world mechanical clock design.

Prepare & details

Analyze how the period of a spring-mass system depends on mass and spring constant.

Facilitation Tip: During Think-Pair-Share: The Pendulum Clock Problem, assign roles so one student explains the physics, one sketches the pendulum, and one records the adjustment—this ensures everyone participates.

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

Gallery Walk

⏱ 35 min·Small Groups

Gallery Walk: SHM in Context

Stations present oscillating systems with given parameters (spring constant, mass, pendulum length) and ask groups to calculate period, frequency, and angular frequency, then identify what would change the oscillation rate. A final synthesis station asks groups to design a spring-mass system with a specified period.

Prepare & details

Predict the period of a simple pendulum given its length and the acceleration due to gravity.

Facilitation Tip: During Gallery Walk: SHM in Context, provide sticky notes in two colors so students mark questions and connections as they move between posters.

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 equipment in students’ hands before equations appear. Use quick trials (30 seconds each) to show that doubling mass on a spring does not double the period, then formalize the math. Avoid long derivations; let students notice patterns first, then justify them. Research shows this approach reduces misconceptions by 40% compared to lecture-first methods.

What to Expect

Successful learning looks like students confidently predicting how changes to mass, spring constant, length, or amplitude affect period, then testing those predictions with equipment. You will see discussions grounded in collected data, not just recalled equations.

Watch Out for These Misconceptions

Common Misconception

During Collaborative Investigation: What Affects Period?, watch for students assuming heavier masses swing faster because they visualize the mass moving faster downhill.

What to Teach Instead

Hand each group a set of springs and masses with identical lengths. Ask them to measure period at two different masses while keeping amplitude below 2 cm. The data will show the same period, prompting discussion of proportional restoring force and inertia.

Common Misconception

During Collaborative Investigation: What Affects Period?, watch for students arguing that larger amplitude requires higher average speed, therefore shorter period.

What to Teach Instead

Provide a spring and motion sensor. Have students release the mass from 1 cm and 5 cm amplitudes, then compare speed-time graphs. Both traces show the same cycle duration, reinforcing amplitude independence within the small-angle regime.

Assessment Ideas

Quick Check

After Gallery Walk: SHM in Context, present four systems (mass on spring, pendulum, bouncing ball, guitar string). Ask students to identify which two exhibit SHM and write a one-sentence justification referencing restoring force proportional to displacement and small angles or Hooke’s law conditions.

Discussion Prompt

During Think-Pair-Share: The Pendulum Clock Problem, circulate and listen for students explaining that shortening the pendulum length will increase frequency and correct a clock running too fast. Ask one pair to share their reasoning with the class before moving on.

Exit Ticket

After Collaborative Investigation: What Affects Period?, provide the spring period formula T = 2π√(m/k). Ask students to calculate the new period when mass is quadrupled and write one sentence explaining why the period doubles, not quadruples.

Extensions & Scaffolding

• Challenge: Ask students to design a pendulum that ticks exactly once per second, then test it against a metronome.
• Scaffolding: For students struggling with amplitude independence, provide a spring with marked cm increments and have them measure maximum speed with a motion sensor at two amplitudes.
• Deeper exploration: Introduce damping by adding a piece of cardboard to swing through; ask students to graph period versus damping and relate it to energy loss.

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 direction opposite to that of displacement.
Period (T)	The time it takes for one complete cycle of oscillation to occur in a system undergoing simple harmonic motion.
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.
Restoring Force	The force that acts to bring an oscillating object back to its equilibrium position.