Lesson plan of Simple Harmonic Motion: Simple Pendulum

Objectives (5 - 7 mins)

1. Introduce the concept of Simple Harmonic Motion (SHM): The teacher should explain to the students what Simple Harmonic Motion is and what its main characteristics are. This includes the definition of a simple pendulum, considering that SHM is the basis of the study of the pendulum.

2. Understand the equation of the simple pendulum: The teacher should present the equation that describes the movement of a simple pendulum, including the influence of the length of the wire and the acceleration of gravity. Students should be able to understand how changes in these parameters affect the movement of the pendulum.

3. Apply SHM to solving problems with simple pendulums: Students should be able to apply the simple pendulum equation to solve practical problems, such as calculating the oscillation period or the angular velocity of a pendulum under different conditions.

   • Secondary Objectives:
     • Develop analytical and critical thinking skills.
     • Encourage the systematic and methodical resolution of problems.
     • Promote the understanding and application of mathematical concepts in physics.

   During the Introduction of these Objectives, the teacher should contextualize the importance of SHM and the simple pendulum, showing students how these concepts are applied in various areas of science and technology, such as in the construction of clocks, for example.

Introduction (10 - 15 mins)

1. Review of relevant content: The teacher should start the class by reviewing some important concepts that are the basis for the study of Simple Harmonic Motion (SHM). These concepts may include the idea of force, mass, acceleration, and energy, as well as a brief review of the concept of motion, including circular motion. This review is essential for students to understand the new content that will be presented.

2. Initial problem situations:

   • Situation 1: The teacher can present a situation where a pendulum is modified in its length and the students need to predict how this change will affect its movement. For example, if the length of the pendulum is doubled, what happens to its oscillation period?
   • Situation 2: The teacher can then present a situation where the pendulum is kept at the same length, but is taken to a location where the acceleration of gravity is different. Students should predict how this change will affect the movement of the pendulum.

3. Contextualization: The teacher should then contextualize the importance of the study of SHM and the simple pendulum, explaining how these concepts are applied in various areas of science and technology. For example, the pendulum is the basis for the construction of clocks and chronometers, and the understanding of SHM is crucial for the prediction and control of many natural phenomena.

4. Introduction to the topic:

   • Curiosity 1: The teacher can share the curiosity that the pendulum was originally used to measure time, before the invention of mechanical clocks. Galileo Galilei, a famous Italian physicist and astronomer, was one of the first to study the pendulum and to propose the idea that its movement is a form of SHM.
   • Curiosity 2: Next, the teacher can mention that, although the pendulum is generally associated with a wall clock, it is present in many other places in our daily lives. For example, pendulums are used in scales to measure mass and in seismographs to measure earthquakes.
   • Practical application: Finally, the teacher can present a practical application of the pendulum and SHM, such as the use of pendulums in physics experiments to demonstrate the conservation of energy or to measure the acceleration of gravity in different locations.

Development (20 - 25 mins)

1. Simple Harmonic Motion (SHM) Theory: (8 - 10 mins)

   • Definition of SHM: The teacher should begin by presenting the theory of SHM, explaining that it is a periodic motion that can be described by a single equation.
   • Characteristics of SHM: Next, the teacher should explain the main characteristics of SHM, such as amplitude, period, and frequency.
   • SHM Equation: The teacher should then present the equation that describes SHM, with emphasis on the relationship between position, amplitude, frequency, and time.
   • SHM Graph: Finally, the teacher should show a graph of an SHM, explaining how the amplitude and frequency are represented.

2. Simple Pendulum: (7 - 9 mins)

   • Definition of the Simple Pendulum: The teacher should introduce the concept of the simple pendulum, explaining that it is an object suspended by an inextensible and massless thread.
   • Simple Pendulum Equation: The teacher should present the equation that describes the movement of a simple pendulum, including the influence of the length of the wire and the acceleration of gravity.
   • Interpretation of the Equation: The teacher should explain how the simple pendulum equation can be interpreted, highlighting the importance of the length of the wire and the acceleration of gravity in the movement of the pendulum.
   • Applications of the Simple Pendulum: The teacher should present some applications of the simple pendulum in everyday life and in science, such as in the construction of clocks and in the measurement of the acceleration of gravity.

3. Solving Problems with the Simple Pendulum: (5 - 6 mins)

   • Example 1: The teacher should present a problem involving the simple pendulum, such as calculating the oscillation period of a pendulum of a certain length at a location with a specific acceleration of gravity. The teacher should then, step by step, guide the students in solving the problem, explaining each step.
   • Example 2: Next, the teacher should present a more complex problem, such as calculating the angular velocity of a pendulum at a specific point in its oscillation. The teacher should again guide the students in solving the problem, explaining each step.

Throughout the Development of the class, the teacher should encourage the active participation of the students, asking questions to check the understanding of the concepts presented and stimulating the discussion in the classroom. In addition, the teacher should remind the students that practice is essential for the understanding and application of SHM and the simple pendulum, and should therefore encourage the resolution of additional problems and exercises.

Feedback (8 - 10 mins)

1. Group discussion: (3 - 4 mins)

   • The teacher should propose a group discussion, where the students will have the opportunity to share their conclusions and solutions to the problems presented in the Development stage.
   • During the discussion, the teacher should encourage the students to explain their answers, justifying them based on the concepts of SHM and the simple pendulum that were presented.
   • The teacher should also clarify any doubts that may arise during the discussion, deepening the students' understanding of the subject.

2. Connection with the real world: (2 - 3 mins)

   • The teacher should then propose that the students reflect on how the concepts of SHM and the simple pendulum can be applied in the real world.
   • For example, students can discuss how the understanding of SHM is fundamental for the construction of clocks and chronometers, or how the simple pendulum equation can be used to calculate the acceleration of gravity in different locations.
   • The teacher should encourage the students to think about other possible applications and share them with the class.

3. Individual reflection: (2 - 3 mins)

   • Finally, the teacher should propose that the students make an individual reflection on what they have learned in the class.
   • The teacher can ask questions such as: "What was the most important concept you learned today?" and "What questions have not yet been answered?"
   • The students should have a minute to think about these questions, and then, if they feel comfortable, they can share their answers with the class.
   • This final reflection is an opportunity for students to consolidate their learning and for the teacher to identify possible gaps in the class's understanding, which can be addressed in future classes.

Throughout the Feedback, the teacher should create a welcoming and respectful environment, where students feel comfortable sharing their opinions and doubts. The teacher should also reinforce the importance of continuous study and practice in the understanding and application of the concepts of SHM and the simple pendulum.

Conclusion (5 - 7 mins)

1. Summary of the Contents: (2 - 3 mins)

   • The teacher should recap the main points covered during the class, recalling the definition and characteristics of Simple Harmonic Motion (SHM), the equation that describes this movement, and the importance of SHM in describing the movement of a simple pendulum.
   • The teacher should emphasize how the simple pendulum equation allows the prediction and control of its movement, and how the length of the wire and the acceleration of gravity influence this movement.
   • It is important that the teacher reinforces the relationship between the theory presented and its practical application, reminding students that the concepts of SHM and the simple pendulum are fundamental in various areas of science and technology.

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

   • The teacher should emphasize how the class connected the theory of SHM and the simple pendulum with practice, through the resolution of problems and exercises.
   • In addition, the teacher should recall the practical applications presented during the class, highlighting how the concepts learned are used in the real world, such as in the construction of clocks and in the measurement of the acceleration of gravity.

3. Extra Materials: (1 min)

   • The teacher should suggest extra materials for students who wish to deepen their knowledge on the subject. These materials may include reference books, educational videos, physics websites, and additional exercises.
   • The teacher should encourage the students to explore these materials at their own pace, reinforcing the importance of autonomous study and practice for effective learning.

4. Importance of the Subject: (1 min)

   • Finally, the teacher should emphasize the importance of studying SHM and the simple pendulum for the students' daily lives.
   • The teacher can mention that, although it may seem like an abstract concept, SHM and the simple pendulum are fundamental to the functioning of many devices that we use daily, such as clocks, scales, and even some toys.
   • In addition, the teacher should emphasize that the understanding and application of these concepts are essential for good performance in physics and in many other scientific disciplines.