Contextualization

Theoretical Introduction

Simple Harmonic Motion (SHM) is a fundamental concept in the study of Physics and refers to a specific type of periodic oscillation. This movement is characterized when the acceleration of a particle, or a body, is directly proportional and opposite to its displacement in relation to an equilibrium position.

SHM is mathematically described by a sinusoidal or cosinusoidal function, with the simple pendulum and the mass-spring system as classical examples. This type of movement is very important for the understanding of various areas of physics, such as sound waves, light, and many other physical phenomena.

Additionally, understanding SHM is crucial for comprehending the laws of physics that govern the motion of bodies. The study of this concept allows the understanding of natural phenomena, as well as the functioning of mechanical, electrical, and electronic devices and systems present in our daily lives.

Contextualization

SHM can be found in various situations in our daily lives. Musical instruments, such as the tuning fork, or machine and vehicle components, like automotive shock absorbers, are governed by this principle.

Moreover, SHM is fundamental for the understanding of numerous technological and scientific innovations, from the simplest applications, such as the movement of a clock pendulum, to the most complex, such as studying the behavior of subatomic particles in particle accelerators.

Practical Activity

Title: "The Pendulum Dance and the Spring Music: Understanding SHM"

Project Objective

Demonstrate the practical application of theoretical knowledge about SHM, linking it with the discipline of mathematics, aiming to create an interdisciplinary and collaborative experience.

Project Description

Groups will be formed by 3 to 5 students and should carry out two practical activities to explore different aspects of SHM. The first activity is themed "Galileo's Pendulum" and the second, "Spring Oscillation".

These activities require the direct application of the theoretical knowledge acquired about the properties and characteristics of SHM, establishing a parallel with mathematical concepts (such as sinusoidal and cosinusoidal functions).

The total duration of the project should be approximately 24 hours per student over two weeks.

Required Materials

For Galileo's Pendulum:

• Resistant cord or string
• Heavy object to serve as the pendulum mass (e.g., a marble or a key)
• Ruler or measuring tape
• Stopwatch
• Support to hang the pendulum (can be a hanger, a nail on the wall, etc.)

For Spring Oscillation:

• Spring
• Various weights (common everyday objects)
• Ruler or measuring tape
• Stopwatch

Step by Step

Galileo's Pendulum

1. Attach the chosen object to the cord, forming the pendulum, and hang it on a support.
2. Measure and record the distance between the support and the center of the pendulum mass.
3. Displace the pendulum mass at a small angle and release it to start oscillating.
4. Use the stopwatch to measure the time it takes for the pendulum to complete a full cycle of oscillation (back and forth). Do this several times and calculate the average time.
5. Repeat steps 3 and 4 with different cord lengths.
6. Create a graph of the oscillation period versus the cord length.

Spring Oscillation

1. Suspend the spring from a support.
2. Hang an object of known weight on the spring and let the spring stabilize.
3. Pull the object down, stretching the spring, and release it to start oscillating.
4. Use the stopwatch to measure the time it takes for the spring to complete a full cycle of oscillation (back and forth). Do this several times and calculate the average time.
5. Repeat steps 3 and 4 with different weights.
6. Create a graph of the oscillation period versus the weight of the object.

Deliverables and Report

After completing the practical activities, students must write a detailed report. This text should cover four main topics:

1. Introduction: Brief contextualization of SHM, its relevance, and real-world applications. Project objectives.
2. Development: Detailed explanation of the two practical activities carried out, describing the methodology used, discussing the theory involved, and analyzing the results of the experiments. Include tables of measurement records and the graphs created.
3. Conclusion: Recap the discussed SHM concepts and the main observations revealed by the practical activities. Reflect on the learning obtained and how the activity contributed to a better understanding of the subject.
4. Bibliography: Citing the sources of information used in the project preparation.

The report must be submitted digitally and formatted according to ABNT standards, with a maximum of 10 pages.