About

Bungee Oscillation

Activities

Translations

Code	Language		Translator	Run

Credits

Leong Tze Kwang; Lawrence Wee Loo Kang; Francisco Esquembre; Felix Garcia Clemente

Overview:

This briefing document reviews information from the Open Educational Resources / Open Source Physics @ Singapore website, specifically focusing on the "Horizontal Spring Energy Displacement Graph" interactive simulation and the broader context of the website as a resource for physics education. The website provides a vast collection of open-source physics applets and simulations designed to enhance learning and teaching. The "Horizontal Spring Energy Displacement Graph" model allows users to explore the relationship between energy and displacement in a mass-spring system.

Main Themes and Important Ideas/Facts:

• Interactive Physics Learning Tool: The core offering highlighted is an interactive HTML5 applet simulation titled "Horizontal Spring Energy Displacement Graph." This tool is designed to visually demonstrate the energy transformations in a horizontal spring system. The description explicitly states, "A cart is attached to a spring." This suggests a classic physics scenario involving kinetic and potential energy exchange.
• Adjustable Variables for Exploration: A key feature of the simulation is the user's ability to manipulate several parameters. The website mentions that when the simulation is running, the user can adjust:
• Amplitude: This refers to the maximum displacement of the cart from its equilibrium position, directly impacting the total energy of the system.
• Spring Constant: This value (often denoted as 'k') determines the stiffness of the spring and influences the potential energy stored at a given displacement.
• Mass of the cart: The mass (often denoted as 'm') affects the kinetic energy of the cart at a given velocity.
• Starting position of the cart: This initial condition influences the initial distribution of potential and kinetic energy.
• Display of each graph: This likely allows users to visualize different forms of energy (e.g., kinetic energy, potential energy, total energy) as a function of displacement or time.
• Open Educational Resource (OER): The website's title and prominent placement under "Open Educational Resources / Open Source Physics @ Singapore" underscore its commitment to providing free and accessible educational materials. The presence of a Creative Commons Attribution-Share Alike 4.0 Singapore License further reinforces this, indicating that the content can be shared and adapted with proper attribution.
• Part of a Broader Collection: The "Horizontal Spring Energy Displacement Graph" is just one of many interactive resources available on the platform. The extensive list of other applets covers a wide range of physics topics, from mechanics and thermodynamics to electromagnetism and optics. This suggests the website serves as a comprehensive repository for physics simulations. Examples from the list include:
• "🤸Horizontal spring dynamics HTML5 Applet Javascript" - A related simulation focusing on the motion itself.
• "📊Horizontal spring energy graph HTML5 Applet Javascript" - Likely a static graph complementing the dynamic simulation.
• Numerous other simulations covering diverse topics like projectile motion, waves, electricity, and even interdisciplinary applications.
• Developed by Educators: The "Credits" section acknowledges "Leong Tze Kwang; Lawrence Wee Loo Kang; Francisco Esquembre; Felix Garcia Clemente" as the creators. This suggests that the resources are developed by individuals with expertise in physics education, implying a pedagogical focus in their design.
• Support for Teachers and Learning Goals: The inclusion of sections like "Sample Learning Goals" and "For Teachers" highlights the website's intention to be a valuable tool for educators. The "Initial Setup" link (https://sg.iwant2study.org/ospsg/index.php/981Direct Link) likely provides guidance on how to use the simulation in a classroom setting.
• Accessibility and Embeddability: The provision of an "Embed" code (using an <iframe> tag) demonstrates a commitment to making the simulation easily integrable into other online learning platforms, websites, or learning management systems.
• Recognition and Impact: The website notes that it was "Recommended in Journal Paper as One of the Top Three Websites for COVID-19 virtual labs education." This suggests the platform gained recognition for its role in providing valuable remote learning resources during the pandemic, highlighting its quality and utility.
• Focus on Interactive Learning: The sheer number and variety of interactive applets underscore a strong emphasis on active learning through exploration and visualization of physics concepts. The use of HTML5 and JavaScript ensures cross-platform compatibility and accessibility through web browsers.
• Connections to Educational Initiatives: The frequent mention of "SLS Hackathon" suggests a connection to Singapore's Student Learning Space (SLS) initiative, indicating that these resources are likely being developed and utilized within the local educational context.

Quotes:

• "A cart is attached to a spring." (From the "Initial Setup" description) - This clearly defines the physical system being modeled in the "Horizontal Spring Energy Displacement Graph" simulation.
• "User is able to adjust these various variables. Amplitude, Spring Constant, the Mass of the cart, the starting position of the cart, and the display of each graph." (From the "For Teachers" section) - This highlights the interactive nature of the simulation and the parameters that users can control to explore the system's behavior.

Conclusion:

The Open Educational Resources / Open Source Physics @ Singapore website, exemplified by its "Horizontal Spring Energy Displacement Graph" simulation, offers a valuable collection of interactive tools for physics education. The platform emphasizes open access, user interactivity through adjustable parameters, and pedagogical relevance for both students and teachers. The wide range of available simulations covering diverse physics topics and its recognition as a key resource for virtual learning underscore its significant contribution to STEM education. The "Horizontal Spring Energy Displacement Graph" specifically provides a dynamic and visual way for learners to understand the fundamental concepts of energy conservation and transformation in a simple harmonic oscillator system.

Horizontal Spring Energy Displacement Study Guide

Overview

This study guide focuses on the concepts related to the horizontal spring energy displacement model provided by Open Educational Resources / Open Source Physics @ Singapore. The resource features an interactive simulation that allows users to explore the relationship between energy, displacement, and other variables in a horizontal spring system with an attached cart. Understanding this model involves grasping the principles of simple harmonic motion, potential and kinetic energy, and the conservation of energy.

Key Concepts

• Simple Harmonic Motion (SHM): The oscillatory motion of an object where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. A horizontal spring-mass system ideally exhibits SHM when friction and other external forces are negligible.
• Displacement (x): The distance of the cart from its equilibrium position.
• Amplitude (A): The maximum displacement of the cart from its equilibrium position.
• Spring Constant (k): A measure of the stiffness of the spring, indicating the force required to stretch or compress the spring by a unit length (F = -kx, where F is the spring force).
• Mass (m): The mass of the cart attached to the spring.
• Potential Energy (U): The energy stored in the spring due to its compression or extension from its equilibrium position. For a spring, potential energy is given by U = (1/2)kx².
• Kinetic Energy (K): The energy of motion of the cart, given by K = (1/2)mv², where v is the velocity of the cart.
• Total Mechanical Energy (E): The sum of the potential and kinetic energies in the system. In an ideal system without energy loss, the total mechanical energy remains constant (E = U + K = constant).
• Energy Displacement Graph: A graphical representation showing how potential energy, kinetic energy, and total energy of the horizontal spring-mass system vary with the displacement of the cart from its equilibrium position.

Interacting with the Simulation

The provided iframe link embeds an interactive simulation. Users can typically:

• Adjust the Amplitude: This changes the maximum displacement of the cart and thus the total energy of the system.
• Adjust the Spring Constant: This affects the stiffness of the spring and the potential energy stored at a given displacement.
• Adjust the Mass of the cart: This influences the kinetic energy of the system at a given velocity and the system's inertia.
• Adjust the Starting position of the cart: This sets the initial displacement and affects the initial potential and kinetic energies.
• Display individual graphs:** Users can likely choose to view graphs of potential energy vs. displacement, kinetic energy vs. displacement, and total energy vs. displacement.

Learning Goals

Based on the provided text, a sample learning goal is to understand how adjusting variables like amplitude, spring constant, and mass affects the energy displacement graph of a horizontal spring system.

Quiz

Answer the following questions in 2-3 sentences each.

1. What type of motion does an ideal horizontal spring-mass system exhibit, and what is the primary condition for this type of motion?
2. Define potential energy in the context of a horizontal spring system. How is it mathematically related to the spring's displacement and spring constant?
3. What is kinetic energy in the context of the cart attached to the spring? How does the velocity of the cart relate to its kinetic energy?
4. Explain the principle of conservation of mechanical energy for an ideal horizontal spring-mass system. What does this imply about the relationship between potential and kinetic energy during oscillation?
5. Describe what the amplitude of oscillation represents in the context of the horizontal spring-mass system. How does changing the amplitude affect the total energy of the system?
6. How does increasing the spring constant of the spring affect the potential energy stored in the system at a given displacement? What are the implications for the forces involved?
7. If the mass of the cart attached to the spring is increased, how would this affect its kinetic energy at the same velocity? What are some other dynamic properties that would change?
8. What information can be gleaned from a graph of potential energy versus displacement for a horizontal spring system? What shape does this graph typically have?
9. What happens to the kinetic energy of the cart when it reaches its maximum displacement (amplitude) in the absence of friction? Explain your reasoning.
10. How does the total mechanical energy appear on an energy displacement graph for an ideal horizontal spring system, and why does it have this appearance?

Quiz Answer Key

1. An ideal horizontal spring-mass system exhibits simple harmonic motion (SHM). This occurs when the restoring force exerted by the spring is directly proportional to the displacement of the mass from its equilibrium position and acts in the opposite direction.
2. Potential energy in a horizontal spring system is the energy stored in the spring due to its being stretched or compressed. It is mathematically given by U = (1/2)kx², where k is the spring constant and x is the displacement from the equilibrium position.
3. Kinetic energy in this system is the energy possessed by the moving cart due to its velocity. It is calculated using the formula K = (1/2)mv², where m is the mass of the cart and v is its instantaneous velocity.
4. The principle of conservation of mechanical energy states that in an ideal system without non-conservative forces like friction, the total mechanical energy (the sum of potential and kinetic energy) remains constant. This means that as potential energy increases, kinetic energy decreases, and vice versa, while their sum stays the same.
5. The amplitude of oscillation is the maximum displacement of the cart from its equilibrium position during its motion. Increasing the amplitude of oscillation increases the total mechanical energy of the system because the maximum potential energy (and thus the total energy) is proportional to the square of the amplitude.
6. Increasing the spring constant of the spring increases the potential energy stored in the system at a given displacement. This is because a stiffer spring (higher k) exerts a greater restoring force for the same amount of stretch or compression.
7. If the mass of the cart is increased, its kinetic energy at the same velocity will also increase because kinetic energy is directly proportional to mass (K = (1/2)mv²). A larger mass will also result in a lower frequency of oscillation for the spring-mass system.
8. A graph of potential energy versus displacement for a horizontal spring system shows how the stored energy in the spring changes as the cart moves. This graph typically has a parabolic shape (U ∝ x²), with the minimum potential energy at the equilibrium position (x=0).
9. At the maximum displacement (amplitude), the velocity of the cart is momentarily zero as it changes direction. Therefore, the kinetic energy of the cart at this point is also zero, and all the energy in the system is in the form of potential energy.
10. On an energy displacement graph for an ideal horizontal spring system, the total mechanical energy appears as a horizontal line. This is because the total energy remains constant regardless of the displacement, as there are no energy losses in the ideal system.

Essay Format Questions

1. Discuss the interplay between potential energy and kinetic energy in a horizontal spring-mass system undergoing simple harmonic motion. Explain how energy is continuously transformed between these two forms during one complete cycle of oscillation, relating your explanation to the cart's position and velocity.
2. Explain how the amplitude and spring constant of a horizontal spring-mass system independently affect the total mechanical energy of the system. Derive the relationship between total energy, amplitude, and spring constant, and discuss the physical implications of this relationship.
3. Consider a real-world horizontal spring-mass system where frictional forces are present. Describe how friction would affect the total mechanical energy of the system over time and how this would manifest on an energy displacement graph. Contrast this with the behavior of an ideal, frictionless system.
4. Analyze the role of mass in the oscillations of a horizontal spring-mass system. Discuss how changing the mass affects the system's frequency of oscillation and its kinetic energy at different points in the motion, assuming the total energy remains constant.
5. Describe the process of setting up and using the provided interactive simulation to investigate the relationship between the adjustable variables (amplitude, spring constant, mass, starting position) and the resulting energy displacement graphs. Explain how this simulation can enhance understanding of the theoretical concepts associated with horizontal spring oscillations.

Glossary of Key Terms

• Equilibrium Position: The natural resting position of the cart attached to the spring where the spring exerts no net force on the cart.
• Oscillation: The repetitive back-and-forth motion of the cart around its equilibrium position.
• Frequency (f): The number of complete oscillations that occur per unit of time, typically measured in Hertz (Hz).
• Period (T): The time required for one complete oscillation. It is the reciprocal of frequency (T = 1/f).
• Restoring Force: The force exerted by the spring that always acts to return the cart to its equilibrium position. It is proportional to the displacement and in the opposite direction (Hooke's Law: F = -kx).

Sample Learning Goals

[text]

For Teachers

 

https://sg.iwant2study.org/ospsg/index.php/981

Direct Link

Research

[text]

Video

[text]

 Version:

1. https://weelookang.blogspot.com/2020/07/horizontal-spring-energy-displacement.html

Other Resources

[text]