Objectives (5 - 7 minutes)

1. Understand the concept of Simple Harmonic Movement (SHM) and its relevance in Physics. Students must be able to define SHM, identify the factors that characterize it and distinguish between harmonic and non-harmonic movements.

2. Identify and describe the characteristics of SHM. Students must be able to identify the main characteristics of SHM, such as the restoring force, the period and frequency, the amplitude and the phase.

3. Understand the conservation of mechanical energy in a SHM. Students must be able to explain how the kinetic and potential energies convert into each other along a SHM and how the total mechanical energy remains constant.

Secondary Objectives:

1. Develop the ability to relate theory to practice through solving problems and discussing concrete examples.

2. Stimulate critical thinking and analytical ability by exploring the applications of SHM in real contexts.

3. Promote students' active participation by encouraging questions and discussions during the class.

Introduction (10 - 15 minutes)

1. Revision of previous concepts: The teacher begins the class by reviewing the concepts of periodic and oscillatory movement, as well as the concepts of kinetic and potential energy. These reviews are essential for students to understand the new topic that will be covered. (3 - 5 minutes)

2. Presentation of problem situations: The teacher proposes two situations for the students:

   • Situation 1: Imagine a ball attached to a spring that is pulled and released. The ball begins to move back and forth. How can we mathematically describe this movement?

   • Situation 2: Now, imagine that the ball from the previous example is on an inclined plane. How does that affect the ball's movement? Is mechanical energy always conserved? (5 - 7 minutes)

3. Contextualization of the importance of the subject: The teacher explains how Simple Harmonic Movement is a crucial concept in Physics, being applied in several areas, such as in the engineering of suspension bridges, in studies of seismic movements and even in the description of natural phenomena, such as the movement of waves in the ocean. (2 - 3 minutes)

4. Introduction to the topic with curiosities: To arouse students' interest, the teacher can share some curiosities:

   • Curiosity 1: Simple Harmonic Movement is so common in nature that it is considered one of the fundamental movements of the universe, along with uniform rectilinear motion and uniform circular motion.

   • Curiosity 2: The concept of SHM was introduced by Galileo Galilei, who observed the movement of a pendulum and noticed that, even if the amplitude of the movement varied, the time to complete an oscillation remained constant. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Explanation of the theory (10 - 12 minutes)

   1.1. Definition of Simple Harmonic Movement: The teacher begins the class explaining that Simple Harmonic Movement is a periodic movement that occurs when the restoring force is directly proportional to the displacement of the object and always acts in the opposite direction to the displacement. (2 - 3 minutes)

   1.2. Characteristics of SHM: The teacher should emphasize that in SHM, the restoring force is always proportional to the displacement, which results in a sinusoidal movement. In addition, the teacher should explain the concepts of amplitude, period, frequency and phase, and how they are related in SHM. (3 - 4 minutes)

   1.3. Equations of SHM: The teacher should present the equations that describe SHM, including the displacement equation, the velocity equation and the acceleration equation. The teacher should demonstrate how these equations are derived and how they are used to describe the movement in SHM. (3 - 4 minutes)

2. Solving problem situations (5 - 7 minutes)

   2.1. Recap of problem situations: The teacher should go back to the problem situations presented in the Introduction and, based on the theory explained, discuss how SHM applies to each of them. For example, in situation 1, the teacher should explain how the restoring force of the spring results in a SHM. In situation 2, the teacher should discuss how the inclination of the plane affects the characteristics of the SHM. (2 - 3 minutes)

   2.2. Application of the SHM equations: The teacher should demonstrate how the equations of SHM can be used to solve the proposed problems. For example, in situation 1, the teacher can ask students to calculate the amplitude, period and frequency of the SHM. In situation 2, the teacher can ask students to calculate the mechanical energy of the system and discuss whether it is conserved. (3 - 4 minutes)

3. Discussion and clarifications (5 - 6 minutes)

   3.1. The teacher should encourage students to ask questions and to discuss their doubts and difficulties. The teacher should clarify any concepts that the students have not fully understood.

   3.2. The teacher should emphasize the importance of understanding SHM, as it is the basis for understanding many other physical phenomena, such as waves and vibrations.

   3.3. The teacher should conclude the explanation of the theory by reinforcing the main points and concepts and preparing the students for the next stage of the class. (2 - 3 minutes)

Feedback (8 - 10 minutes)

1. Connection with the real world (3 - 4 minutes)

   1.1. The teacher should highlight how Simple Harmonic Movement is an essential part of many aspects of everyday life and technology. For example, the principles of SHM are applied in many engineering devices, such as suspension bridges, pendulum clocks, musical instruments, among others.

   1.2. The teacher can ask students to think about other examples of SHM in their daily lives or in technologies they use. For example, students may mention the movement of a seesaw, the movement of a pendulum in a wall clock, or the movement of a tuning fork in a musical instrument.

   1.3. The teacher should emphasize that understanding SHM is not only important for academic success, but also for appreciating the world around us.

2. Reflection on learning (2 - 3 minutes)

   2.1. The teacher should ask students to reflect on what they have learned during the class. Students can think about the following questions:

    - What was the most important concept you learned today?
    - What questions have not yet been answered?
   

   2.2. The teacher can ask some students to share their answers with the class. This not only helps to consolidate what was learned, but also allows the teacher to evaluate the effectiveness of the class and make adjustments for the next time.

3. Feedback and evaluation of the class (2 - 3 minutes)

   3.1. The teacher should request feedback from students about the class. Feedback can be collected informally through questions such as "What did you think of the class?" or "What did you find most useful?"

   3.2. The teacher should evaluate the students' performance during the class, observing their participation, understanding of the concepts and their ability to apply the theory to practical situations. This will help the teacher identify areas that may need revision or reinforcement in future classes.

   3.3. The teacher should reinforce that the students' feedback is valued and will be used to improve future classes.

4. Closing the class (1 minute)

   4.1. The teacher should thank the students for their participation and effort.

   4.2. The teacher should remind students about the study material for the next class and encourage them to review the class content at home.

   4.3. The teacher should say goodbye to the students and wish them a good day.

This feedback moment is crucial to consolidate learning, establish connections with the real world, reflect on what was learned and evaluate the effectiveness of the class.

Conclusion (5 - 7 minutes)

1. Content Recap (2 - 3 minutes)

   • The teacher should summarize the main points of the class, recalling the definition of Simple Harmonic Movement (SHM) and its fundamental characteristics.
   • The conservation of mechanical energy in a SHM should be recapitulated, highlighting how kinetic and potential energy convert into each other and how the total mechanical energy remains constant.
   • The teacher should also reinforce the importance of problem-solving and discussing practical examples for understanding SHM.

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

   • The teacher should highlight how the class connected the theory of SHM with practice through problem-solving and discussing real situations.
   • The relevance of SHM in several real-world applications should be reinforced, such as in engineering, particle physics, acoustics, among others.

3. Suggestion of Supplementary Materials (1 minute)

   • The teacher should suggest additional study materials for students who wish to delve deeper into the subject. This may include reference books, physics websites, educational videos, among others.
   • Some recommended resources could be: "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca, "The Physics Classroom" (a physics teaching website with a section dedicated to SHM), and the "Khan Academy" channel on YouTube (which has several videos explaining SHM).

4. Relevance of the Topic for Everyday Life (1 minute)

   • The teacher should conclude the class by emphasizing how SHM is relevant to students' everyday lives.
   • It can be mentioned, for example, how SHM is fundamental to the functioning of several objects and devices that we use daily, such as clocks, musical instruments, toys, among others.
   • In addition, the teacher can emphasize that understanding SHM can help students better understand various natural phenomena, such as the behavior of waves in water or in the air.

The conclusion of the class is a crucial moment to consolidate learning, reinforce the relevance of the topic and direct students to continue their studies. The teacher should ensure that students have a clear and complete understanding of SHM before ending the class.