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Bungee Oscillation

Activities

Translations

Code	Language		Translator	Run

Credits

Francisco Esquembre

Main Themes and Important Ideas/Facts:

1. Fundamental Concepts of Mass-Spring Systems:

The title "Mass and Spring" directly indicates the subject matter, suggesting a discussion of the physical principles governing the interaction between mass and elastic springs.
While the specific content of Esquembre's text is not provided in the excerpt, the title implies an exploration of concepts such as Hooke's Law (the force exerted by a spring is proportional to its displacement), potential and kinetic energy in the system, and the conditions leading to oscillatory motion.

2. Simple Harmonic Motion (SHM):

The title of the second source, "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript," explicitly mentions Simple Harmonic Motion. This indicates that the applet is designed to illustrate systems that exhibit, or can approximate, SHM.
SHM is characterized by a restoring force directly proportional to the displacement from equilibrium, leading to sinusoidal oscillations.

3. Interactive Simulation as a Learning Tool:

The second source is primarily about an "HTML5 Applet Javascript," highlighting the use of interactive simulations for educational purposes.
The presence of an "Embed this model in a webpage:" section with an iframe code snippet demonstrates the intention for this tool to be easily integrated into online learning environments. This underscores the value of hands-on, visual learning in physics education.

4. Bungee Cord as a Model for Oscillation:

The specific focus on "Bungee Oscillation" suggests that the applet models the behavior of a mass attached to a bungee cord. While a bungee cord can exhibit more complex behavior than an ideal spring, under certain conditions (e.g., when stretched), its elastic properties can be approximated by Hooke's Law, leading to oscillatory motion similar to a mass-spring system.

5. Key Controllable Variables:

The "For Teachers" section explicitly states the controllable variables within the applet: "The Controllable variables are the Amplitude, Period, Frequency and Damping Ratio."
Amplitude: The maximum displacement from the equilibrium position.
Period: The time taken for one complete oscillation.
Frequency: The number of oscillations per unit time.
Damping Ratio: A measure of how quickly oscillations decay due to energy dissipation (e.g., air resistance, internal friction).
These variables are fundamental to describing and analyzing oscillatory motion, and the applet allows users to explore their effects.

6. Visualization through Phase Circle and Animation:

The applet utilizes a "phase circle" for display. A phase circle is a graphical representation of the state of an oscillator, showing both its displacement and velocity at a given time as a point moving in a circle.
The description "The right panel will animate to show the phases" indicates a dynamic visualization that helps users understand the temporal evolution of the oscillator's state in the phase space.

7. Open Educational Resources and Credits:

The source is identified as part of "Open Educational Resources / Open Source Physics @ Singapore," emphasizing its accessibility and potential for free use and adaptation in educational settings.
Francisco Esquembre is credited, linking him to the development of this applet, and potentially also to the Easy Java/JavaScript Simulations Toolkit mentioned elsewhere on the page ("Easy Java/JavaScript Simulations Toolkit https://www.um.es/fem/EjsWiki/ vy Francisco Esquembre and Félix Jesús Garcia Clemente"). This suggests a broader contribution to the creation of physics simulations.

8. Sample Learning Goals:

The presence of "[text]" under "Sample Learning Goals" indicates that the full resource likely provides specific learning objectives that the applet is intended to help students achieve. These goals would further clarify the educational focus of the simulation.

9. Links to Related Resources:

The extensive list of links on the page, including "SHM Bungee Acceleration vs Displacement Graph HTML5 Applet Javascript," "Horizontal Spring SVA Graph Javascript," and others related to springs and oscillations, suggests a comprehensive collection of interactive tools for exploring different aspects of oscillatory motion and related concepts.

Quotes from Original Sources:

(From "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript"): "The Controllable variables are the Amplitude, Period, Frequency and Damping Ratio." (For Teachers section)
(From "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript"): "The display is in a phase circle. The right panel will animate to show the phases." (For Teachers section)
(From "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript"): "Embed this model in a webpage: "

Conclusion:

The provided excerpts offer insights into the study of mass-spring systems and simple harmonic motion through both potentially theoretical explanations ("Mass and Spring") and interactive simulations ("SHM Bungee Phase Circle & Damping HTML5 Applet Javascript"). The latter emphasizes the use of technology to visualize abstract physics concepts, allowing students to explore the influence of key parameters like amplitude, period, frequency, and damping on oscillatory behavior within the context of a bungee cord system. The availability of such open educational resources highlights the growing importance of interactive learning tools in physics education.

Study Guide: Mass-Spring Systems and Simple Harmonic Motion

Core Concepts

Oscillation: A repetitive variation, typically in time, of some measure about a central value or between two or more different states.
Simple Harmonic Motion (SHM): A specific type of oscillatory motion where the restoring force is directly proportional to the displacement and acts in the opposite direction.
Mass-Spring System: A physical system consisting of a mass attached to an elastic spring, capable of exhibiting oscillatory motion when disturbed from its equilibrium position.
Equilibrium Position: The position of a mass-spring system where the net force on the mass is zero.
Displacement: The distance of the mass from its equilibrium position at any given time.
Restoring Force: The force exerted by the spring on the mass, which always acts to return the mass to its equilibrium position. According to Hooke's Law, this force is proportional to the displacement ( $F = -kx$ , where $k$ is the spring constant and $x$ is the displacement).
Spring Constant (k): A measure of the stiffness of the spring. A higher spring constant indicates a stiffer spring that requires more force to stretch or compress by a given amount.
Amplitude (A): The maximum displacement of the mass from its equilibrium position during oscillation.
Period (T): The time taken for one complete oscillation or cycle of the motion.
Frequency (f): The number of oscillations or cycles that occur per unit of time. It is the reciprocal of the period ( $f = 1/T$ ).
Angular Frequency (ω): Related to the frequency by the equation $\omega = 2\pi f = 2\pi/T$ . It is often used in mathematical descriptions of SHM.
Phase: A quantity that describes the point in the oscillatory cycle that the system is at a particular time.
Damping: A force that opposes the oscillatory motion and causes the amplitude of the oscillations to decrease over time (e.g., friction, air resistance).
Phase Circle: A graphical tool used to represent the phase and amplitude of SHM, often visualizing the relationship between displacement, velocity, and acceleration as a point moving in a circle.

Quiz

Describe the relationship between the restoring force exerted by a spring and the displacement of the mass in a simple harmonic oscillator. What law governs this relationship?
Define the period and frequency of oscillation in a mass-spring system. How are these two quantities mathematically related to each other?
What is meant by the amplitude of oscillation in SHM? How does it relate to the energy of the oscillating system (without considering damping)?
Explain the concept of equilibrium position in a mass-spring system. What is the net force acting on the mass when it is at this position?
What is the role of the spring constant in determining the characteristics of the oscillations in a mass-spring system? How does a larger spring constant affect the frequency of oscillation?
Briefly describe what is meant by damping in an oscillatory system. What effect does damping have on the amplitude of the oscillations over time?
What is a phase circle and how is it used to represent simple harmonic motion? What information about the oscillation can be gleaned from a phase circle diagram?
According to the provided sources, who is credited with the creation of the "Mass and Spring" resource and the "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript"?
The "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript" lists "Controllable variables." Name at least three of these variables that can be adjusted in the simulation.
The Open Educational Resources / Open Source Physics @ Singapore website provides a wide array of interactive resources. Besides oscillations, list two other physics-related topics for which applets or simulations are available, based on the provided text.

Quiz Answer Key

The restoring force exerted by a spring in a simple harmonic oscillator is directly proportional to the displacement of the mass from its equilibrium position and acts in the opposite direction. This relationship is governed by Hooke's Law, which states that $F = -kx$ , where $F$ is the restoring force, $k$ is the spring constant, and $x$ is the displacement.
The period (T) of oscillation is the time required for one complete cycle of the oscillatory motion to occur. The frequency (f) of oscillation is the number of complete cycles that occur per unit of time. They are inversely related by the equation $f = 1/T$ .
The amplitude (A) of oscillation is the maximum displacement of the mass from its equilibrium position during one cycle of SHM. It represents the extent of the oscillation. The amplitude is directly related to the total energy of the system; a larger amplitude corresponds to a higher total energy.
The equilibrium position in a mass-spring system is the location where the spring is neither stretched nor compressed, and consequently, the net force acting on the mass is zero. At this position, the restoring force from the spring is balanced by any other constant forces (like gravity if the system is oriented vertically, though not explicitly mentioned in the excerpts for a horizontal spring).
The spring constant (k) determines the strength of the restoring force for a given displacement. A larger spring constant means a stiffer spring and a stronger restoring force, leading to a higher frequency of oscillation ( $f \propto \sqrt{k}$ ).
Damping is a force that opposes the motion of an oscillator, such as friction or air resistance. Damping causes the mechanical energy of the oscillating system to be gradually converted into other forms of energy (like heat), resulting in a decrease in the amplitude of the oscillations over time until they eventually cease.
A phase circle is a circular diagram where a rotating vector represents the state of a simple harmonic oscillator. The length of the vector corresponds to the amplitude, and the angle of the vector with respect to a reference axis represents the phase of the oscillation. Projecting the vector onto the horizontal or vertical axis gives the displacement or velocity as a function of time.
Francisco Esquembre is credited with the creation of both the "Mass and Spring" resource and the "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript" according to the provided information.
Three controllable variables listed for the "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript" are Amplitude, Period, and Frequency. The Damping Ratio is also mentioned as a controllable variable.
Based on the provided text, other physics-related topics for which applets or simulations are available include Newtonian Mechanics (as the oscillation applet falls under this category), Elasticity, Electromagnetism, and topics related to waves (Standing & Longitudinal waves).

Essay Format Questions

Discuss the relationship between the restoring force, displacement, and the resulting simple harmonic motion in a mass-spring system. Explain how the spring constant affects the period and frequency of these oscillations.
Compare and contrast the concepts of period, frequency, and angular frequency in the context of simple harmonic motion. How are these quantities mathematically interconnected, and what do they physically represent in the oscillation of a mass-spring system?
Explain the phenomenon of damping in oscillatory systems, providing examples of damping forces. Discuss the effect of damping on the amplitude and energy of a mass-spring system undergoing simple harmonic motion.
Describe the utility of a phase circle in visualizing and understanding simple harmonic motion. Explain how the phase circle represents key parameters such as amplitude, phase, displacement, and velocity of an oscillating mass.
Based on the provided text about the "SHM Bungee Phase Circle & Damping HTML5 Applet Javascript," discuss the potential educational benefits of using such interactive simulations for learning about oscillations and simple harmonic motion. Consider the role of controllable variables and visual representations in student understanding.

Glossary of Key Terms

Amplitude (A): The maximum extent of an oscillation or vibration, measured from the position of equilibrium.
Angular Frequency (ω): A scalar measure of rotation rate, often expressed in radians per second. For SHM, $\omega = 2\pi f$ .
Damping: The dissipation of energy from an oscillating system, usually due to resistive forces, causing the amplitude to decrease over time.
Displacement (x): The distance and direction of an object from its equilibrium position.
Equilibrium Position: The stable position where the net force acting on an object is zero.
Frequency (f): The number of complete cycles of an oscillation per unit of time, typically measured in Hertz (Hz).
Hooke's Law: A law stating that the force needed to extend or compress a spring by a distance $x$ is proportional to that distance: $F = -kx$ .
Mass-Spring System: A physical system consisting of a mass attached to a spring, capable of oscillating when disturbed.
Oscillation: A repetitive variation over time of some measure about a central value or between two or more different states.
Period (T): The time taken for one complete cycle of an oscillation. It is the reciprocal of frequency ( $T = 1/f$ ).
Phase: The fraction of a cycle that has elapsed at a particular time, often expressed as an angle in radians.
Phase Circle: A graphical representation of simple harmonic motion using a rotating vector whose projection onto an axis represents the displacement.
Restoring Force: A force that acts to bring an object back to its equilibrium position.
Simple Harmonic Motion (SHM): A type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
Spring Constant (k): A measure of a spring's stiffness, defined as the force per unit extension or compression.

Sample Learning Goals

[text]

For Teachers

Initial Setup. The Controllable variables are the Amplitude, Period, Frequency and Damping Ratio. The display is in a phase circle.

The right panel will animate to show the phases.

Research

[text]

Video

[text]

Version:

Other Resources

[text]

Frequently Asked Questions

1. What is Simple Harmonic Motion (SHM) as implied by the provided resources?

Simple Harmonic Motion (SHM), as suggested by the resources, is a type of oscillatory motion where the restoring force is directly proportional to the displacement and acts in the opposite direction. The "Mass and Spring" title directly refers to a classic system that exhibits SHM. The "SHM Bungee Phase Circle & Damping" applet further indicates the study of SHM in the context of a bungee cord system, likely exploring concepts like oscillations, phase circles, and damping effects on SHM.

2. What kind of interactive tools and simulations are highlighted in these resources?

The "Open Educational Resources / Open Source Physics @ Singapore" source heavily emphasizes interactive HTML5 applets and JavaScript simulations for learning physics and other subjects. Numerous examples are listed, covering topics from mechanics (like oscillations, springs, projectiles) and electromagnetism to chemistry, math, and even language games. These tools allow users to manipulate variables and observe the resulting changes in real-time, fostering a hands-on learning experience. The mention of "Easy JavaScript/Java Simulations Toolkit (EJS)" and its license further underscores the focus on creating and utilizing such interactive content.

3. What are some of the physics concepts that these simulations specifically address?

The listed applets cover a wide range of physics concepts, including:

Oscillations and Waves: SHM, bungee oscillations, standing and longitudinal waves, wave superposition.
Mechanics: Newton's laws, projectile motion, forces, energy (kinetic, potential, thermal), friction, torque, elasticity, fluid mechanics (buoyancy, air drag), rotational motion (spinning gyroscope).
Electromagnetism: Magnetic fields, electromagnets, electromagnetic waves, mass spectrometer.
Optics: Diffraction, laser beam profiles, polarization.
Thermodynamics: Heat transfer, heat loss and gain, kinetic theory of gases.
Relativity: Relativistic dynamics.
Quantum Mechanics/Atomic Physics: Bohr's theory of the hydrogen atom.

4. Who are the key individuals or groups involved in creating and sharing these resources?

Francisco Esquembre is explicitly credited in both "Mass and Spring" and the "SHM Bungee Phase Circle & Damping" applet, indicating his significant contribution to these simulations. Open Educational Resources / Open Source Physics @ Singapore is the main platform hosting many of these resources. Wolfgang Christian is also mentioned in relation to Open Source Physics and Optics Bench JS. The Easy JavaScript Simulations Toolkit is credited to Francisco Esquembre and Félix Jesús Garcia Clemente. Various teachers and students from Singapore schools are also mentioned as creators of specific hackathon projects.

5. What is the pedagogical approach behind these resources?

The emphasis on interactive simulations, open educational resources, and the numerous examples of games and activities suggests a strong focus on active learning, exploration, and visualization of abstract concepts. The resources aim to make learning more engaging and accessible through hands-on manipulation and immediate feedback. The inclusion of "Sample Learning Goals" and sections "For Teachers" in the applet descriptions indicates an intent to support educators in using these tools effectively in their teaching.

6. How are these resources being used or recognized in the educational community?

The mention of the "2020 Excellence in Physics Education Award from American Physical Society goes to Open Source Physics Team" and the recommendation in a journal paper as "One of the Top Three Websites for COVID-19 virtual labs education" highlight the significant recognition and impact of these resources within the physics education community. The numerous hackathon projects and teacher attachments to MOE HQ-ETD suggest active use and development of these tools within the Singaporean education system.

7. What subjects beyond physics are covered by the resources listed?

While physics is a central theme, the resources also extend to other subjects, including:

Mathematics: Geometry (area, perimeter, trigonometry), algebra, calculus (implied in some physics models), number theory (prime numbers, GCD), statistics (dice throw).
Chemistry: Atomic structure, stoichiometry, chemical bonding, organic molecules, periodic trends, X-ray crystallography, balancing chemical equations, electrolysis.
Biology: Life cycles, food webs, COVID-19 virus spread.
Computer Science: Programming concepts (sorting algorithms).
Economics: Taxes, production possibility curve.
Language Arts: Chinese and Malay vocabulary games, sentence scrambling, alliteration identification, simile and metaphor games, rhyming games.

8. What is the licensing and accessibility of these resources?

The "Mass and Spring" resource mentions a release under a license (specific details not provided in the excerpt). The Open Educational Resources / Open Source Physics @ Singapore explicitly states that "Contents are licensed Creative Commons Attribution-Share Alike 4.0 Singapore License." This indicates that the materials are freely available for use and adaptation, provided attribution is given and any derivative works are shared under a similar license. The platform is presented as a collection of "Open Educational Resources," emphasizing its commitment to free and accessible educational materials. Commercial use of the EasyJavaScriptSimulations Library requires a separate license.

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Details: Written by Siti; Parent Category: 02 Newtonian Mechanics; Category: 09 Oscillations; Published: 24 July 2020; Created: 24 July 2020; Last Updated: 31 March 2025; Hits: 2881

Oscillations