Objectives (5 - 7 minutes)

1. Understanding of Simple Harmonic Motion: The main goal is that students understand the concept of Simple Harmonic Motion (SHM), comprehending the relation between the movement of an object and the force that acts upon it.

2. Identification of SHM Elements: Students must be able to identify the elements that compose SHM, such as amplitude, period, frequency, and phase.

3. Mechanical Energy Analysis in SHM: The third objective is that students be able to analyze mechanical energy in SHM, understanding how potential and kinetic energies vary along the movement.

Secondary objectives:

• Practical Application of SHM: Besides the theory, students must be able to apply SHM to practical problems, using the formula and concepts learned to solve problem situations.

• Discussion and Debate: Encourage students to actively participate in discussions and debates about the topic, promoting comprehension and a deeper understanding of the subject.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher starts the class by reviewing previous concepts that are fundamental to the comprehension of the topic, such as the concept of movement, force, and energy. They can suggest questions for the students to think and discuss in groups, reviewing concepts and setting the stage for the Introduction of Simple Harmonic Motion (SHM).

2. Problem Situations: Then, the teacher proposes two problem situations that involve SHM. The first situation can involve the movement of a simple pendulum, asking students about the regularity of that movement. The second situation can be the graphic representation of a compressed spring movement, asking the students what that representation would look like.

3. Contextualization: The teacher explains the importance of studying SHM in several fields, such as engineering (when designing bridges and buildings that must withstand earthquakes), medicine (when studying the movement of internal organs), and music (when studying sound waves). They can also mention how SHM is present in daily life phenomena, such as the movement of a clock's pendulum.

4. Capturing Attention: To spark the students' interest, the teacher can share curiosities about SHM. For instance, they can mention that the movement of a pendulum is used in atomic clocks, the most precise in the world. Another curiosity is that SHM is present in the movement of several organs of the human body, such as the heart and the lungs. Additionally, they can mention that music is, in essence, the combination of several simple harmonic movements, due to the phenomenon of resonance.

Development (20 - 25 minutes)

1. Activity "Building a Pendulum":

   • Material Preparation: The teacher organizes the students into groups of 3 or 4 people and gives each group a string, a marble, and a ruler. Each group must have a space to do the activity.
   • Activity Description: The teacher explains that the students will build a simple pendulum and, then, measure the time it takes for the marble to complete a full oscillation. This will allow them to calculate the pendulum's period.
   • Activity Execution: The students follow the teacher's instructions to build the pendulum, adjusting the string's height and the marble's mass. Then, each group makes the necessary measurements and writes down the results.
   • Discussion and Analysis: After all groups are done, the teacher promotes a classroom discussion, asking the students about what they observed and how the height and the mass affect the pendulum's period. Then, the teacher introduces the mathematical formula for the pendulum's period and explains that this is an example of Simple Harmonic Motion.

2. Activity "Experimenting with a Spring":

   • Material Preparation: The teacher gives each group a spring and a set of masses with different weights.
   • Activity Description: The teacher explains that the students will study the behavior of a spring when subjected to different forces. They will measure the spring's deformations and the applied force and then calculate the spring's elastic constant.
   • Activity Execution: Each group makes the necessary measurements, following the teacher's instructions. They write down the results and calculate the spring's elastic constant.
   • Discussion and Analysis: Once all the groups are done, the teacher promotes a classroom discussion, asking the students about their observations and the relation between the force and the spring's deformation. Then, the teacher introduces the potential elastic energy formula and explains that this is another example of Simple Harmonic Motion.

3. Activity "Solving SHM Problems":

   • Material Preparation: The teacher distributes to each group a sheet with exercises involving SHM.
   • Activity Description: The teacher explains that the students will have to solve the problems, applying the concepts and formulas they learned during class.
   • Activity Execution: The students, in their groups, solve the proposed problems.
   • Discussion and Analysis: After a set amount of time, the teacher promotes a classroom discussion, asking the students about the strategies used to solve the problems and clearing up possible doubts.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • Sharing Solutions: Each group, in a pre-determined order, shares their solutions or conclusions from the activities "Building a Pendulum" and "Experimenting with a Spring". The teacher must encourage the students to explain how they reached their conclusions and relate them to the SHM and mechanical energy concepts previously discussed.
   • Connection with Theory: After each presentation, the teacher should ask questions that help connect the students' findings to the theory. For instance, "How did the height of the pendulum or the marble's mass affect the oscillation period?" or "How is the force applied to the spring related to its deformation and potential elastic energy?".

2. Individual Reflection (2 - 3 minutes):

   • Reflection Moment: The teacher asks the students to think about what they learned in class, individually. They must think about the answers to the following questions:
     1. What was the most important concept learned today?
     2. What questions are still unanswered?
   • Reflection Recording: Students write down their answers in a notebook or piece of paper.

3. Sharing Reflections (3 - 5 minutes):

   • Reflection Discussion: The teacher then asks a few students to share their reflections with the class. The teacher should promote a discussion, asking questions that will help clarify the students' doubts and reinforce the concepts learned.
   • Recording Questions: The teacher must also record the questions that have not been answered to approach them in future classes or content reviews.

4. Teacher's Feedback (2 - 3 minutes):

   • General Feedback: The teacher concludes the class by providing general feedback, reinforcing the most important concepts, praising the students' efforts, and encouraging them to keep studying and practicing. The teacher must also mention the most common questions and the areas that students need to focus on to improve their understanding of SHM.
   • Preparing for the Next Class: The teacher must then briefly introduce the topic of the next class, explaining how it connects to what was learned today and which skills or concepts students will need for the next class.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes):

   • The teacher begins the Conclusion by reviewing the main points discussed during class. They recap the concept of Simple Harmonic Motion (SHM), the importance of identifying SHM elements, and analyzing mechanical energy in this type of movement.
   • The teacher makes a brief summary of the practical activities conducted, highlighting the results obtained and how they relate to theory. They reinforce the practical application of SHM, showing how the theoretical concepts were used to solve real-life problems.

2. Connection Between Theory, Practice, and Applications (1 - 2 minutes):

   • The teacher emphasizes the importance of connecting the theory to the practice and applications of SHM. They highlight how the practical activities helped the students visualize and better understand the theoretical concepts and how such concepts are applied in several fields of knowledge and in daily life.
   • The teacher reinforces that physics is not only a theoretical discipline, but a science that can be used to explain and predict natural and technological phenomena.

3. Supplementary Materials (1 minute):

   • The teacher suggests complementary study materials for the students who wish to deepen their knowledge about SHM. They can recommend books, websites, videos, simulations, and apps that provide explanations and exercises about the topic. They can also point to chapters in textbooks or other resources that can be useful to review the class's content.

4. Importance of the Subject (1 minute):

   • Finally, the teacher stresses the importance of SHM in the real world. They mention that understanding SHM is essential in several areas of science and engineering, such as acoustics, optics, fluid mechanics, structural engineering, among others.
   • The teacher also highlights that the ability to solve problems related to SHM is a valuable skill, not only for physics but also for developing analytical skills, logical thinking, and problem-solving skills that can be applied to many situations in daily life and academia.