Lesson Plan | Active Learning | Simple Harmonic Motion: Equation of Motion

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 minutes)

This stage of the lesson plan is crucial for establishing the necessary foundations for students to understand and apply concepts related to simple harmonic motion. By clearly defining the objectives, students can focus on the essential skills that will be developed and assessed during the class. This helps ensure that all participants are aligned and prepared for the practical exercises and discussions that will follow.

Main Objectives:

1. Formulate a simple harmonic motion equation, detailing the steps for constructing the motion equation.

2. Identify and analyze whether a body is performing simple harmonic motion or not, using mathematical and physical criteria.

Side Objectives:

1. Develop analytical skills in physics by applying mathematical concepts to solve physical problems.
2. Promote scientific communication skills through the discussion of results and methods with peers.

Introduction

Duration: (20 minutes)

The introduction serves to engage students with the content through problem situations that stimulate reflection on prior study and to highlight the relevance of simple harmonic motion in real life. This initial moment is crucial for activating students' prior knowledge, in addition to contextualizing the importance of the concepts that will be explored, making learning more meaningful and applicable.

Problem-Based Situations

1. A simple pendulum is released from a small height. How can you predict the behavior of the pendulum over time using the concept of simple harmonic motion?

2. A spring is suspended vertically with an object attached to its end. When pulled down and released, the object begins to oscillate. What variables are necessary to describe this movement and how do they influence the oscillation?

Contextualization

Simple harmonic motion is a phenomenon that frequently occurs in nature and technological applications, from pendulum clocks to vehicle suspension systems. Understanding this type of motion not only deepens physical knowledge but also enhances the ability to innovate and solve practical problems. Furthermore, studying this topic allows students to understand how physical concepts are applied in real-life situations, such as in bridge engineering and musical acoustics, where vibrations play a fundamental role.

Development

Duration: (75 - 85 minutes)

The development stage in the lesson plan is designed to provide students with a practical and interactive experience to apply the theoretical concepts studied about simple harmonic motion. Through playful and contextualized activities, this part of the plan aims to consolidate learning through experimentation and analysis, allowing students to visualize and physically manipulate the principles of simple harmonic motion. These activities are also designed to foster teamwork and analytical skills, essential for a deeper understanding of physics.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Spectacular Oscillation

> Duration: (65 minutes)

- Objective: Apply knowledge of simple harmonic motion to deduce physical properties through practical experimentation.

- Description: In this activity, students will be challenged to build and analyze a simple pendulum to understand the equation of simple harmonic motion. The class will be divided into groups of up to 5 members, where each group will build its own pendulum using a rope and a mass. They will measure the oscillation time for different lengths of rope and masses, recording their data for later analysis.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the necessary materials: ropes, various masses, stopwatches.

• Instruct students to assemble the pendulum by fixing the rope to a support and tying the mass to the other end.

• Ask each group to measure the oscillation period of the pendulum for 5 different lengths of rope, recording the data.

• Students should use the formula for the pendulum period to calculate the gravitational constant and compare it with the theoretical value.

Activity 2 - Magic Spring

> Duration: (60 minutes)

- Objective: Investigate how different masses affect the characteristics of simple harmonic motion in a spring.

- Description: Students will explore simple harmonic motion through a vertically suspended spring with a mass at the end. Each group will change the mass and measure the frequency and amplitude of the movement, creating a report on the relationship between mass, frequency, and amplitude.

- Instructions:

• Organize students into groups of up to 5.

• Provide each group with a spring, a set of masses, and a timing measurement device.

• Guide students to attach an initial mass to the spring and allow it to oscillate freely after being stretched.

• Instruct groups to record the frequency and amplitude of oscillation for each mass used.

• Students should plot the data and analyze how mass affects the frequency and amplitude of oscillations.

Activity 3 - The Dance of Pendulums

> Duration: (70 minutes)

- Objective: Understand how the pendulum length influences the oscillation period and explore the concepts of phase and synchronization in simple harmonic motion.

- Description: In this playful scenario, students will investigate how different lengths of pendulums affect their oscillation period. They will create multiple pendulums and perform a 'pendulum concert', observing the synchrony and phase of the oscillations and relating them to the theory of simple harmonic motion.

- Instructions:

• Divide the room into groups of up to 5 students.

• Hand each group ropes of various lengths and small masses to be used as weights.

• Ask the groups to assemble pendulums with each length of rope and suspend them side by side.

• Instruct students to start all the pendulums at the same time and observe the differences in the oscillations.

• Students should record the oscillation periods and discuss how the length of the rope affects the motion.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to allow students to reflect on their practical and theoretical learning, consolidating the knowledge acquired through group discussion. This feedback session is crucial for students to articulate what they learned, identify gaps in their understanding, and apply knowledge critically and analytically. Furthermore, by sharing their experiences and results, students develop communication skills and learn to value different approaches and solutions to the same physical problem.

Group Discussion

Start the group discussion with a brief review of the experiments conducted. Ask students how they applied the theory of simple harmonic motion in practice and what observations they found most interesting or surprising. Encourage them to share unique insights or challenges encountered during the practical activities. Ask how the equations of simple harmonic motion helped predict and understand the behaviors observed in the experiments.

Key Questions

1. How does the theory of simple harmonic motion apply to the behavior of the pendulums and springs you tested?

2. What factors did you find that significantly affect the oscillation of the systems you constructed?

3. How did you use the equations to calculate practical results, such as the gravitational constant or the frequency of oscillations?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage of the lesson plan is to consolidate learning by reiterating the key concepts and practical experiences that students have undergone. This synthesis helps reinforce the knowledge acquired and understand how to apply theory and practice in an integrated manner. Additionally, by highlighting the importance of simple harmonic motion in practical applications, we encourage students to perceive physics as a living science present in everyday life.

Summary

In this conclusion, we will review the fundamental concepts of simple harmonic motion covered during the class. We will recap how the motion equation was deduced and applied in practical examples such as pendulums and springs, consolidating theoretical understanding with experimental practice.

Theory Connection

The connection between theory and practice was established through experimental activities, where students were able to visualize and quantify the behavior of oscillatory systems. This not only reinforced the understanding of mathematical equations but also highlighted the importance of analytical and critical thinking in solving real problems.

Closing

Finally, we emphasize the relevance of simple harmonic motion in various everyday and technological applications, such as in bridge engineering, musical acoustics, and vehicle damping systems, demonstrating how physics concepts apply practically and essentially in our daily lives.