Context

This project, related to the study of Physics, considers two fundamental concepts: Simple Harmonic Motion (SHM) and Uniform Circular Motion (UCM). Simple Harmonic Motion is a type of oscillatory motion that occurs when the resulting force acting on the particle is proportional and contrary to the equilibrium displacement. UCM is one in which an object moves along a circle with constant speed.

These concepts may seem abstract at first, but they are visible and applicable in many aspects of our daily lives. Both SHM and UCM are fundamental parts of many mechanisms, from the simplest, such as a swing in a park, to the most complex, such as the operation of an engine.

Both types of movements are mathematically described by sinusoidal functions, and it is this property that allows a direct relationship to be established between them. This means that any SHM can be interpreted as a projection of UCM. This connection between two different concepts of movements allows a deeper understanding of both and stimulates analytical thinking and the ability to make theoretical connections.

Introduction

The study of Simple Harmonic Motion is the basis for understanding numerous physical phenomena that we find in nature, such as, for example, the movement of a pendulum, an oscillating spring or even the sound waves produced by a musical instrument. Learning to describe and predict these movements is a valuable skill in physics.

Uniform Circular Motion, in turn, is a basic concept for understanding how objects move around a central point. This is the type of movement performed by the planets around the sun, for example, but it can also be observed in a carousel toy or in the wheel of a bicycle.

By understanding the relationship between SHM and UCM, students will be able to map one movement onto the other, expanding their analytical skills and creating a link between concepts learned separately.

To deepen the study and understanding of these concepts, it is recommended to consult the following resources:

• YouTube: “Física Universitária” Channel, available at: https://www.youtube.com/user/fisicauniversitaria.
• Book: “Fundamentals of Physics” - Volume 2, by Halliday, Resnick, Walker, 9th edition.
• Website: Khan Academy - Physics sections on SHM and UCM, available at: https://www.khanacademy.org/science/physics.

Practical Activity: Simulating Movements

Project Objective

Students must demonstrate the equivalence between SHM and UCM by creating a practical simulation.

Project Description

The project consists of creating a physical simulation of a simple harmonic motion (SHM), such as a pendulum or an oscillating spring, and representing this movement in a circumference, demonstrating the equivalence with a uniform circular motion (UCM).

Required Materials

1. An object to create the SHM (such as a spring or a pendulum).
2. Graph paper to plot and record the movement.
3. Python or Processing programming environment, for digital simulation (optional).

Step by step

1. Students should divide into groups of 3 to 5 people.
2. The first step is to create the SHM. It can be a pendulum tied to the ceiling or a spring hung with a weight at the end.
3. Once the SHM is working, students should observe and discuss the characteristics of the movement.
4. After observation and discussion, students should try to record the movement on a graph, using graph paper.
5. The next step is to create a representation of the UCM. Students must then draw a circumference on the graph paper and “project” the movements of the SHM in the circumference, thus demonstrating the equivalence of the SHM with the UCM.
6. If possible, students should create a code in Python or Processing to digitally simulate what they did physically.
7. At the end of the project, students should prepare a detailed report of the work done.

Project Deliveries

Students will deliver:

• Manual graphs of SHM and UCM, demonstrating the equivalence between them.

• Digital simulation code, if performed.

• A written report of the work. This report should be divided into four parts:

  1. Introduction: Here students should contextualize the project, explaining the concept of SHM and UCM, the relationship between them and their practical application. The objective of the project should also be clearly stated in this part.
  2. Development: In this section, students should detail the theory of SHM and UCM and describe in detail the activities carried out, including the entire process of building the SHM and representing the UCM. They should also explain the methods used to carry out the activities and present and discuss the results obtained.
  3. Conclusion: The conclusion should include a recap of the main parts of the project, as well as the lessons learned and the conclusions drawn about the project.
  4. Bibliography: Students should list the sources they used to work on the project, such as textbooks, websites and videos.

The time foreseen for the execution of the project is two to four hours for each student and the deadline is one week from the date of presentation of the activity.