Lesson Plan | Active Learning | Simple Harmonic Motion: Relationship between SHM and UCM

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 - 7 minutes)

The objective stage is crucial for directing the focus of students and the teacher towards the expected learning outcomes. By clearly establishing what is expected to be achieved, both in terms of theoretical knowledge and practical skills, students can better understand the importance of the study of Simple Harmonic Motion and its relationship with Uniform Circular Motion. This clarity helps maximize the effectiveness of class time, ensuring that all activities are aligned with the learning objectives.

Main Objectives:

1. Enable students to relate simple harmonic motion (SHM) to uniform circular motion (UCM), identifying their similarities and differences.

2. Develop calculation skills and practical application when calculating speeds and deformations in SHM and UCM systems.

Side Objectives:

1. Awaken students' interest in physics through practical and everyday applications of SHM and UCM concepts.

Introduction

Duration: (15 - 20 minutes)

The purpose of the Introduction stage is to engage students with problem situations that utilize previously studied concepts about Simple Harmonic Motion and Uniform Circular Motion, stimulating the practical application of knowledge. Furthermore, the contextualization aims to connect theoretical content with the real world, increasing interest and awareness of the importance of the topics addressed. This approach aims to prepare students for the practical activities that will follow and for classroom discussions.

Problem-Based Situations

1. Consider a simple pendulum on a roller coaster, where the cart moves in a circular path. How can we use the concept of Simple Harmonic Motion to describe the motion of the pendulum in this context?

2. Imagine a computer hard drive that uses an actuator to position the read/write head over different circular tracks. How can the analysis of Uniform Circular Motion help us understand the vibrations that may occur and the importance of Simple Harmonic Motion in this scenario?

Contextualization

The study of Simple Harmonic Motion (SHM) and its connection with Uniform Circular Motion (UCM) is essential not only in theoretical physics but also in practical applications of everyday life. For example, the operation of clocks, subways, motors, and even information technologies, like hard drives, directly depend on these principles. Additionally, understanding these concepts helps to comprehend natural phenomena, such as the motion of planets and galaxies. This contextualization helps students visualize the relevance and ubiquity of these phenomena in the real world.

Development

Duration: (70 - 75 minutes)

The Development stage is designed to allow students to practically and concretely apply the concepts of Simple Harmonic Motion (SHM) and its relationship with Uniform Circular Motion (UCM). Through playful and interactive activities, students will have the opportunity to explore these concepts in contexts that simulate real-world situations, reinforcing learning and encouraging creativity and teamwork. This stage aims to solidify the theoretical knowledge acquired at home and prepare students for more in-depth discussions and critical analyses in the classroom.

Activity Suggestions

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

Activity 1 - The Dancer of the Hard Drive

> Duration: (60 - 70 minutes)

- Objective: Understand and simulate the motion of a hard drive read/write head, relating it to the concepts of SHM and UCM.

- Description: In this activity, students will simulate the operation of a computer hard drive, where the read/write head moves along circular tracks. The idea is for students, divided into groups, to use a simple disk model (which can be made with cardboard and a needle) and a control system (which can be a system of strings and weights) to move the needle along a circular path while observing and controlling the frequency and amplitude of the motion.

- Instructions:

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

• Distribute the necessary materials to assemble the hard drive model and control system.

• Guide students to assemble the disk model, insert the 'needle' and connect the control system.

• Ask them to adjust the system to simulate different frequencies and amplitudes of motion.

• Instruct students to record observations and measure the parameters of the motion (frequency, amplitude).

• Each group should present their observations and discuss the relationships with SHM and UCM.

Activity 2 - Pendulum on the Roller Coaster

> Duration: (60 - 70 minutes)

- Objective: Explore the properties of simple harmonic motion in a roller coaster context and reinforce the connection with uniform circular motion.

- Description: Students will design and build a small pendulum model that simulates the motion on a roller coaster. Using lightweight materials like nylon strings and small masses, they will adjust the model to replicate simple harmonic motion. This practical exercise will allow students to directly observe and control the properties of SHM and its relation to UCM.

- Instructions:

• Organize students into groups and provide construction materials (strings, masses, lightweight supports).

• Guide students to design and assemble the pendulum model, ensuring it can be adjusted for different amplitudes and frequencies.

• Instruct groups to conduct tests with the pendulum, varying the conditions and recording data for each configuration.

• Ask each group to analyze the collected data and make a presentation on how SHM can be observed in their experiment.

• Lead a class discussion to compare different observations and discuss the applications of SHM and UCM in the context of pendulums and roller coasters.

Activity 3 - Resonance Circuit

> Duration: (60 - 70 minutes)

- Objective: Visualize simple harmonic motion in an electronic system and understand its practical applications.

- Description: In this activity, students will build a simple electrical circuit that includes an oscillator and a resonance detection system. They will use an oscilloscope to visualize the resonance frequency of the system and will manually adjust the frequency to observe the effects of simple harmonic motion. This exercise will help connect the concepts of SHM with practical applications in electronics and engineering.

- Instructions:

• Divide the class into groups and distribute the electrical circuit assembly kits, including oscillators and oscilloscopes.

• Guide students in assembling the circuit, explaining the basic operation of each component.

• Instruct groups to adjust the frequency of the oscillator to find the resonance in the system and observe the harmonic motion generated.

• Ask each group to record their observations and present the results to the class.

• Lead a discussion on how SHM concepts are applied in engineering and modern technology.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate students' practical learning, allowing them to share their experiences and learn from one another. The group discussion helps reinforce understanding of the concepts of SHM and UCM, as well as develop communication and reasoning skills. This moment also serves to clarify any remaining doubts and for the teacher to assess the effectiveness of the activities conducted, ensuring that learning objectives have been achieved.

Group Discussion

After completing the practical activities, gather all students in a large circle for a group discussion. Start the session with a brief introduction, emphasizing the importance of sharing discoveries and insights. Explain that each group will have the opportunity to briefly present what they discovered and discuss the connections between Simple Harmonic Motion (SHM) and Uniform Circular Motion (UCM) in their experiments. Encourage students to express their opinions and to listen attentively to their peers, fostering an environment of respect and collaboration.

Key Questions

1. What were the biggest challenges when trying to relate SHM to UCM in your activities?

2. How do the properties of amplitude and frequency affect the behavior of the systems you simulated?

3. What practical applications of SHM and UCM can you identify from the examples we studied or in other everyday contexts?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to solidify the knowledge acquired during the lesson, ensuring that students can clearly articulate what they have learned and how it applies in real and theoretical contexts. Additionally, this stage serves to reinforce the link between theory and practice, highlighting the relevance of studies in SHM and UCM in practical and everyday applications, and preparing students for possible extensions of learning in their future academic and professional lives.

Summary

In the conclusion stage, the teacher should summarize and recap the main points addressed regarding Simple Harmonic Motion (SHM) and its relationship with Uniform Circular Motion (UCM). It is essential to reinforce the concepts of amplitude, frequency, speed, and acceleration, highlighting how they manifest in the studied systems, such as the pendulum, the hard drive, and the resonance circuit.

Theory Connection

Today's lesson was structured to effectively connect theory and practice. Through practical activities, students were able to observe, manipulate, and directly measure the physical phenomena discussed in class, such as the behavior of SHM and its relation to UCM. This not only solidified theoretical understanding but also demonstrated the applicability of the concepts in real situations, such as the operation of technological devices and mechanical systems.

Closing

Finally, it is crucial to highlight the importance of studying SHM and UCM in everyday life. These concepts not only have direct applications in fundamental technologies, such as hard drives and clocks, but also help to understand complex natural phenomena, such as the motion of planets. Understanding these physical principles allows for a deeper appreciation of the world around us and prepares students for future studies and practical applications.