Bungee SHM Study Guide

Review Questions

1. What are the key physical principles underlying Simple Harmonic Motion (SHM)?
2. How does the presence of a bungee cord modify the conditions for pure SHM in an oscillating system?
3. What are the key variables that describe the motion of an object undergoing Bungee SHM, and how do they relate to each other?
4. How can a phase circle graph be used to represent and analyze SHM? What information does it provide?
5. According to the provided materials, what controllable variables are available in the "SHM Bungee Phase Circle Graph HTML5 Applet"?
6. What is the purpose of visualizing Bungee SHM using an animation alongside a phase circle graph?
7. Based on the title of one of the sources ("Bungee SHM"), what does the acronym SHM stand for in this context?
8. Who are the authors credited for the "Bungee SHM" document and the "SHM Bungee Phase Circle Graph HTML5 Applet"?
9. Under what type of license is the "Bungee SHM" document released? What are the implications of this license?
10. What is the stated primary function of the "SHM Bungee Phase Circle Graph HTML5 Applet" as described in the "For Teachers" section?

Quiz

1. Describe the fundamental characteristics of Simple Harmonic Motion. What distinguishes it from other types of oscillatory motion?
2. Explain how the restoring force in a system undergoing SHM is mathematically related to the displacement from its equilibrium position. Provide the relevant equation.
3. In the context of a bungee system, when would the motion approximate pure SHM, and when would the elastic properties of the bungee cord introduce deviations from ideal SHM?
4. What does the radius of the phase circle represent in the context of SHM, and how is the angular velocity on the phase circle related to the frequency of the oscillation?
5. Identify and briefly describe the two controllable variables mentioned for the "SHM Bungee Phase Circle Graph HTML5 Applet." How might changing these variables affect the simulation?
6. Why is the phase difference a useful concept when analyzing oscillatory motion, particularly when comparing the motion of two related objects or aspects of a single object's motion?
7. What are the potential benefits of using an interactive simulation, like the provided HTML5 applet, for learning about Bungee SHM compared to solely studying theoretical descriptions?
8. Based on the credits, what software or environment was used to compile the "Bungee SHM" document? Why might this information be relevant?
9. What does it mean for educational resources to be released under a Creative Commons Attribution-Share Alike license? How does this impact the use and distribution of the "Bungee SHM" material?
10. Briefly explain how the animation of two objects alongside the phase circle graph in the applet could help users understand the relationship between the physical motion and its graphical representation.

Quiz Answer Key

1. Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the equilibrium position. This results in oscillations with a constant period and sinusoidal displacement over time.
2. The restoring force (F) in SHM is directly proportional to the displacement (x) and acts in the opposite direction, represented by the equation F = -kx, where k is the spring constant (or a similar proportionality constant). This linear relationship is a hallmark of SHM.
3. The motion would approximate pure SHM when the bungee cord is taut and behaving like an ideal spring with a linear restoring force. Deviations would occur when the bungee cord slackens (providing no restoring force) or when its elastic properties are non-linear, especially at large extensions.
4. The radius of the phase circle represents the amplitude of the SHM, which is the maximum displacement from the equilibrium position. The angular velocity on the phase circle (ω) is related to the frequency (f) of the oscillation by the equation ω = 2πf.
5. The two controllable variables are the Period and the Phase Difference. Changing the period would affect the time it takes for one complete oscillation. Adjusting the phase difference would introduce a lead or lag in the oscillatory motion being represented, potentially between two objects or between displacement and velocity.
6. Phase difference quantifies the temporal separation between two oscillations or between different aspects of the same oscillation (like displacement and velocity). It helps in understanding how the motions are synchronized or out of sync and can be visualized as the angular separation on a phase circle.
7. Interactive simulations allow users to visualize abstract concepts like SHM and phase relationships in a dynamic way. By manipulating variables and observing the immediate effects on the animation and graph, learners can develop a more intuitive and deeper understanding compared to passive learning from text alone.
8. The "Bungee SHM" document was compiled with EJS 6.1 BETA (Easy JavaScript Simulations). This is relevant because it indicates the software tool used to create the resource, suggesting its potential for interactivity or simulation capabilities, even if not explicitly embedded in the document itself.
9. A Creative Commons Attribution-Share Alike 4.0 license allows others to copy, distribute, display, and perform the work and to make derivative works based on it, provided they give credit to the original authors and license their new creations under identical terms. This promotes open access and collaboration.
10. By showing the physical motion of the objects alongside their corresponding positions on the phase circle, the simulation visually connects the abstract representation of SHM with the concrete movement of the oscillating system. This helps users understand how the angular position and motion on the phase circle relate to the displacement and velocity of the physical objects over time.

Essay Format Questions

1. Discuss the conditions under which a bungee cord system undergoing oscillations can be accurately modeled as Simple Harmonic Motion. What factors would cause deviations from this ideal model, and how might these deviations manifest in the motion?
2. Explain the utility of the phase circle graph in analyzing Simple Harmonic Motion. How do the key parameters of SHM (amplitude, frequency, and phase) relate to the features of a phase circle diagram? Consider how the "SHM Bungee Phase Circle Graph HTML5 Applet" leverages this representation.
3. Compare and contrast the information gained from observing the animation of a Bungee SHM system with the information obtained from its corresponding phase circle graph. How do these two representations complement each other in enhancing understanding of the motion?
4. Based on the provided excerpts, analyze the potential pedagogical benefits of using interactive simulations like the "SHM Bungee Phase Circle Graph HTML5 Applet" for teaching and learning about oscillatory motion. Consider aspects such as visualization, exploration of variables, and engagement.
5. Explore the significance of open educational resources and open-source physics initiatives, as exemplified by the provided materials. How do licenses like Creative Commons Attribution-Share Alike contribute to the accessibility and collaborative development of educational content in physics?

Glossary of Key Terms

• 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 from the equilibrium position. This results in sinusoidal oscillations.
• Oscillation: A repetitive variation, typically in 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 usually measured in seconds.
• Frequency (f): The number of complete cycles of an oscillation that occur per unit time. It is typically measured in Hertz (Hz), where 1 Hz = 1 cycle per second.
• Amplitude (A): The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
• Phase Difference (φ): The difference in phase between two oscillations or between two points on the same oscillation. It describes how much one oscillation leads or lags another in time and is often expressed in radians or degrees.
• Phase Circle Graph: A graphical representation of SHM where the state of the oscillating system (position and velocity) is represented by a vector rotating with a constant angular velocity. The projection of this vector onto the x-axis (or y-axis) represents the displacement as a function of time.
• Restoring Force: A force that acts to bring a system back to its equilibrium position. In SHM, this force is proportional to the displacement.
• Equilibrium Position: The central or neutral position of an oscillating object where the net force acting on it is zero.
• HTML5 Applet: A small application written in HTML5, often using JavaScript, that can be embedded in a webpage to provide interactive content, such as simulations.
• Open Educational Resources (OER): Teaching, learning, and research materials in any medium – digital or otherwise – that reside in the public domain or have been released under an open license that permits no-cost access, use, adaptation, and redistribution by others with no or limited restrictions.
• Open Source Physics (OSP): An initiative that promotes the use and development of open-source computational tools and resources for physics education.
• Creative Commons License: A type of public copyright license that enables the free distribution of an otherwise copyrighted work. Different Creative Commons licenses offer different levels of permission and restriction. Attribution-Share Alike requires users to give credit to the creator and to distribute any derivative works under the same license.