🕰️Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5

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Pendulum Toy

  • Source Type: Software tool compiled with EJS 6.1 BETA.
  • Authorship and Licensing: Developed by a team including This email address is being protected from spambots. You need JavaScript enabled to view it., Fu-Kwun Hwang, Francisco Esquembre, Wolfgang Christian, and Félix J. García. Released under a Creative Commons Attribution license (© 2021). This indicates the tool is likely freely available for use and adaptation with proper attribution.
  • Main Theme: The title suggests this is a digital tool designed for users to interact with and explore the behavior of pendulums. The fact that it is "Compiled with EJS 6.1 BETA" points towards its likely use for creating simulations and visualizations of physical phenomena, possibly for educational purposes.
  • Key Implications: The Creative Commons license makes this a valuable resource for educators looking for open-source tools to demonstrate pendulum motion. The mention of EJS (Easy JavaScript Simulations) suggests the tool is likely interactive and customizable.

2. Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5

  • Source Type: Interactive HTML5 simulation applet accessible online through "Open Educational Resources / Open Source Physics @ Singapore."
  • Authorship: Developed within the context of the Open Educational Resources / Open Source Physics @ Singapore project. Real-time evolution code specifically mentions Shaun.
  • Main Theme: This resource focuses on providing a real-time, interactive simulation of a pendulum, specifically highlighting its connection to Simple Harmonic Motion (SHM). The detailed "Learning Outcomes" and "Learning Experiences" sections clearly indicate its primary purpose is educational.
  • Key Ideas and Facts:
  • Simple Harmonic Motion (SHM): The resource explicitly links the pendulum's behavior (under small angle approximations) to SHM. This is evident in the section title "Simple Harmonic Motion" and the guiding questions like "How can circular motion be related to simple harmonic motion (SHM)?"
  • Learning Outcomes (LOs): A comprehensive list of learning objectives is provided, covering fundamental aspects of oscillations and SHM. These include:
  • Describing free oscillations.
  • Investigating motion graphically and experimentally.
  • Understanding and using terms like amplitude, period, frequency, and angular frequency.
  • Recognizing and using the defining equation of SHM: "a = - ω2 x".
  • Applying solution equations for displacement and velocity: "x= x0 ω sin( ωt )" and "v = v0 cos ( ω t ) , v = ± ω ( x 0 2 - x 2 )".
  • Describing and illustrating changes in displacement, velocity, and acceleration graphically.
  • Explaining the interchange between kinetic and potential energy.
  • Discussing damped and forced oscillations, including resonance and its practical implications. The LO on resonance highlights its dual nature: "show an appreciation that there are some circumstances in which resonance is useful and other circumstances in which resonance should be avoided."
  • Learning Experiences: The resource suggests various interactive activities for students, such as:
  • Examining different graphical representations of SHM.
  • Investigating factors affecting the period of oscillations through experiments or simulations. The text explicitly states: "Investigate factors affecting period of oscillations using experiments or a simulation... This provides an opportunity for students to predict and collect data to ascertain the properties of a system and determine whether a motion is considered to be SHM. Students are also to understand that it is necessary for oscillations to be small for the motion to be considered as SHM." This emphasizes the small angle approximation crucial for SHM.
  • Investigating phase relationships using turntables or simulations, linking SHM to uniform circular motion.
  • Building models of SHM using dataloggers or simulations, focusing on interpreting graphs and understanding variable relationships.
  • Exploring real-world applications, such as molecular oscillations (with small amplitudes) and the benefits and dangers of resonance.
  • Interactive Simulation: The presence of an "Embed" code (<iframe...>) indicates the resource is designed to be easily integrated into web pages, making it highly accessible for online learning. The "Run Sim" link further confirms the interactive nature.
  • Small Angle Approximation: The resource explicitly addresses the limitation of the simple pendulum model for SHM, stating in response to a guiding question: "1.1.2.A1: : 10 degrees for error of , depending on what is the error acceptable, small angle is typically about less than 10 degree of swing from the vertical." This is a crucial point for understanding the validity of the SHM approximation.
  • Code Snippets: The inclusion of JavaScript code snippets (e.g., "// prevTime is initialised when the play button is hit...") suggests transparency in the simulation's underlying mechanics, potentially valuable for advanced learners or educators interested in the computational aspects. The equations within the code (e.g., omega += alpha * dt;) illustrate the numerical integration methods likely used for the real-time evolution.
  • Links to Other Resources: The presence of numerous links to other pendulum simulations (e.g., from Walter Fendt, Phet Colorado) and related concepts (e.g., Conical Pendulum on GeoGebra) broadens the learning opportunities and provides alternative tools for exploration.
  • Applications: The resource mentions applications for various platforms (Android/iOS, Windows/MacOSX/Linux), highlighting its broad compatibility.

Relationship Between the Sources:

While "Pendulum Toy" is presented with less specific detail in the provided excerpt, it likely serves a similar purpose to the "Real Time Evolution Line Code 10 Pendulum" applet – to provide a visual and interactive way to understand pendulum motion. The common authorship (overlapping names in the credits) suggests a potential connection or that both are part of a larger collection of educational physics resources developed by the same team. The "Pendulum Toy" might be a more comprehensive software package, while the "Real Time Evolution" applet is a specific, web-based simulation focusing on SHM aspects.

Educational Implications:

The "Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5" is a rich educational resource for teaching oscillations and Simple Harmonic Motion. Its strengths include:

  • Clearly defined learning outcomes: Educators can easily align their teaching with the specified objectives.
  • Engaging interactive simulation: The ability to run the simulation online and embed it in webpages enhances student engagement and accessibility.
  • Emphasis on conceptual understanding: The guiding questions and suggested learning experiences encourage students to explore and interpret the behavior of pendulums.
  • Integration of theory and practice: The resource connects theoretical concepts of SHM with visual representations and interactive investigations.
  • Addressal of limitations: Explicitly mentioning the small angle approximation is important for developing a nuanced understanding.
  • Links to further exploration: The inclusion of links to other simulations and resources allows students to deepen their learning.

Potential Use Cases:

  • Classroom demonstrations: Teachers can use the embedded simulation to visually illustrate pendulum motion and its relation to SHM.
  • Interactive student activities: Students can explore the simulation independently, investigating the effects of different parameters on the pendulum's period and behavior.
  • Homework and self-study: The online accessibility allows students to review concepts and experiment with the simulation outside of the classroom.
  • Virtual labs: The simulation can serve as a virtual laboratory environment for exploring oscillatory motion.

Conclusion:

The "Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5" is a valuable open educational resource for teaching and learning about pendulums and Simple Harmonic Motion. Its interactive nature, clearly defined learning objectives, and connection to real-world examples make it a powerful tool for educators and students alike. "Pendulum Toy," while less detailed in the provided excerpt, likely complements this resource as a potentially more comprehensive software tool for exploring pendulum dynamics. The shared authorship and Creative Commons licensing further enhance the value and accessibility of these resources for the educational community.

 

Real Time Evolution added by Shaun into the Evolution page

/ Date.now() gets the current UNIX timestamp in milliseconds.
curTime = Date.now();
// prevTime is initialised when the play button is hit. dt measures the time passed between 2 consecutive steps
var dt = (curTime - prevTime) / 1000;

omega += alpha * dt;
theta += omega * dt;
omegas += (-(g/L) * thetas) * dt;
thetas += omegas * dt;

t += dt;

prevTime = curTime;

Apps

https://lh3.googleusercontent.com/vNkGjQMxecJP9GsM4I7XCDVbkDqOr1ULKGyGo4eJlrBdIndPR82ZkdlD9FFFeCNhb58=w300-rwhttps://play.google.com/store/apps/details?id=com.ionicframework.shm01app615913&hl=en

Other Resources

  1.  https://www.geogebra.org/m/sux2Q5ak The Conical Pendulum by ukukuku

Press the play button. Watch the graph to see how the angle of the pendulum changes as it swings back and forth. Use the graph to determine the period of the pendulum. Adjust the scale by dragging the numbers on the axes. Change each variable – gravity, rod length, starting angle and mass – and observe how each one affects the period. Can you explain why? Try the damping slider. Does damping change the period?

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Study Guide: Pendulum Motion and Simple Harmonic Motion

Quiz

Answer the following questions in 2-3 sentences each.

  1. According to the "Pendulum Toy" information, under what condition is the motion of a simple free pendulum accurately described as simple harmonic motion?
  2. What is the typical maximum angle of release (in degrees) for a simple pendulum to maintain approximately simple harmonic motion, as mentioned in the "Pendulum Toy" information?
  3. Based on the "Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5" source, what are the four key terms used to describe oscillations, and what do they generally represent?
  4. The "Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5" source mentions a defining equation for simple harmonic motion. What is this equation, and what do the symbols represent?
  5. One of the learning outcomes listed is the ability to recognize a specific equation as a solution to the defining equation of SHM. What is this equation provided in the source?
  6. According to the learning outcomes, what kind of energy transformation occurs during simple harmonic motion?
  7. The "Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5" source discusses damped oscillations. What key aspect of damping is highlighted as important in systems like a car suspension?
  8. What phenomenon occurs when a system is subjected to a driving frequency that is close to its natural frequency, as described in the learning outcomes?
  9. The "Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5" source suggests using simulations to investigate factors affecting the period of oscillations. Name two variables that can be adjusted in the pendulum simulation mentioned in the "Explore some factors that affect the period of a pendulum" section.
  10. The "Real Time Evolution Line Code 10 Pendulum JavaScript Model Simulation Applet HTML5" source mentions associating SHM with uniform circular motion. What mental links are students encouraged to make through this association?

Quiz Answer Key

  1. The motion of a simple free pendulum is accurately described as simple harmonic motion when the angle of displacement from the vertical is small. This small angle approximation ensures that the restoring force is approximately proportional to the displacement.
  2. The typical maximum angle of release before the motion of a simple pendulum is not accurately described as simple harmonic motion is around 10 degrees. This is because beyond this angle, the restoring force is no longer directly proportional to the displacement.
  3. The four key terms are amplitude, period, frequency, and angular frequency. Amplitude refers to the maximum displacement from equilibrium, period is the time for one complete oscillation, frequency is the number of oscillations per unit time, and angular frequency is related to the rate of change of the phase of the oscillation.
  4. The defining equation of simple harmonic motion is a = - ω² x. In this equation, 'a' represents acceleration, 'ω' represents angular frequency, and 'x' represents displacement from the equilibrium position.
  5. The equation recognized as a solution to a = - ω² x is x = x₀ ω sin(ωt). Here, 'x' is the displacement at time 't', 'x₀' is the amplitude, and 'ω' is the angular frequency.
  6. During simple harmonic motion, there is a continuous interchange between kinetic energy (energy of motion) and potential energy (stored energy due to position). The total mechanical energy of the system remains constant (in the absence of damping).
  7. Critical damping is highlighted as important in cases such as a car suspension system. Critical damping allows the system to return to its equilibrium position in the shortest time possible without oscillating, providing a smooth and controlled ride.
  8. Resonance occurs when a system is subjected to a driving frequency near its natural frequency. This can lead to a significant increase in the amplitude of the forced oscillation, which can be beneficial in some cases and detrimental in others.
  9. Two variables that can be adjusted in the pendulum simulation mentioned are gravity and rod length. Adjusting these variables allows observation of their effects on the period of the pendulum's swing.
  10. Students are encouraged to make mental links between the physical position and velocity of the oscillator, the angle in the associated uniform circular motion, and the position of the oscillator on a displacement-time graph. This helps to visualize and understand the relationships in SHM.

Essay Format Questions

  1. Discuss the relationship between simple harmonic motion and uniform circular motion. How does visualizing SHM as a projection of circular motion aid in understanding the characteristics and equations of SHM? Provide specific examples from the source material to support your explanation.
  2. Analyze the factors that affect the period of a simple pendulum. Based on the provided resources, describe how changes in these factors influence the pendulum's oscillation and explain why the small angle approximation is crucial for the motion to be considered simple harmonic.
  3. Compare and contrast free oscillations, damped oscillations, and forced oscillations. Provide real-world examples of each, including the importance of critical damping and the potential benefits and dangers of resonance as highlighted in the source material.
  4. Explain the interchange between kinetic and potential energy in a system undergoing simple harmonic motion. Describe how these energies vary with displacement and velocity throughout one complete oscillation.
  5. Critically evaluate the use of simulations as a learning tool for understanding simple harmonic motion, as suggested in the provided resources. What are the advantages of using simulations, and how can they help students grasp abstract concepts related to oscillations?

Glossary of Key Terms

  • Amplitude (x₀): The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
  • Period (T): The time taken for one complete cycle of an oscillation or wave. It is the time required for the oscillating system to return to its initial state.
  • Frequency (f): The number of complete cycles of an oscillation or wave that occur per unit time, usually measured in Hertz (Hz), where 1 Hz = 1 cycle per second.
  • Angular Frequency (ω): A measure of the rate of oscillation, expressed in radians per second. It is related to the frequency (f) and period (T) by the equations ω = 2πf = 2π/T.
  • 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. This results in sinusoidal oscillations.
  • Free Oscillation: Oscillations that occur when a system is disturbed from its equilibrium position and then allowed to oscillate without any external forces acting on it (ignoring damping).
  • Damped Oscillation: Oscillations in which the amplitude of motion decreases over time due to energy loss, typically through friction or air resistance.
  • Critical Damping: The specific level of damping that allows a system to return to its equilibrium position in the shortest possible time without oscillating.
  • Forced Oscillation: Oscillations that occur when an external periodic force is applied to a system, causing it to oscillate at the driving frequency of the external force.
  • Resonance: The phenomenon that occurs when the driving frequency of a forced oscillation is close to the natural frequency of the system, resulting in a large increase in the amplitude of the oscillation.
  • Restoring Force: A force that acts to return an oscillating system to its equilibrium position. In SHM, this force is proportional to the displacement.
  • Equilibrium Position: The central or resting position of an oscillating system where the net force acting on it is zero.

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Press the play button. Watch the graphs to see the motion of the spring pendulum. Can you distinguish the pattern of spring motion (up and down) from the pattern of pendulum motion (back and forth)? How are the two related? Is there a regular pattern to the motion? Compare the periods of the two graphs. How many different patterns can you produce by changing the variables – gravity, rod length, mass and spring constant? Under what conditions does the energy switch between back and forth and up and down? Does the initial starting angle affect the patterns when all the other variables are unchanged?

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  1. http://www.walter-fendt.de/html5/phen/pendulum_en.htm 
  2. http://physics.bu.edu/~duffy/HTML5/pendulum.html
  3. https://phet.colorado.edu/en/simulation/pendulum-lab 
  4. http://www.thephysicsaviary.com/Physics/Programs/Labs/PendulumLab/index.html

Frequently Asked Questions about Pendulum Simulations

1. What is a simple pendulum, and what key characteristics describe its motion?

A simple pendulum, in an idealized model, consists of a point mass (the bob) suspended from a fixed point by a massless, inextensible string. When displaced from its equilibrium position and released, it oscillates under the influence of gravity. The key characteristics describing its motion include its period (the time for one complete oscillation), its frequency (the number of oscillations per unit time), its amplitude (the maximum displacement from the equilibrium position), and its angular frequency (related to the rate of change of the angle of displacement).

2. What is Simple Harmonic Motion (SHM), and under what conditions can a pendulum exhibit SHM?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction. Mathematically, it's defined by the equation a = -ω²x. A pendulum approximates SHM when its angle of displacement from the vertical is small (typically less than 10 degrees). In this small-angle approximation, the restoring force (a component of gravity) is approximately proportional to the displacement, leading to oscillations that closely resemble SHM.

3. How can we investigate the factors that affect the period of a pendulum using simulations?

Pendulum simulations allow us to manipulate various parameters such as the length of the rod, the mass of the bob, and the acceleration due to gravity, and observe their effect on the period of oscillation. By running simulations and analyzing the resulting motion (often through graphs of angle vs. time), we can experimentally determine how each factor influences the period. For instance, we can observe that the period of a simple pendulum primarily depends on its length and the acceleration due to gravity, and is largely independent of the mass of the bob (within the small angle approximation).

4. How are concepts like amplitude, period, frequency, and angular frequency used to describe the motion of a pendulum in SHM?

These terms provide a quantitative description of the oscillatory motion. Amplitude defines the extent of the swing. Period (T) is the time taken for one complete cycle. Frequency (f) is the number of cycles per second (f = 1/T). Angular frequency (ω) is related to the frequency by ω = 2πf and represents the rate of change of the angular displacement. In the mathematical description of SHM for a pendulum, these parameters appear in the equations for displacement (x = x₀ sin(ωt + φ)), velocity, and acceleration.

5. How does the energy of a pendulum change during SHM?

During the SHM of a pendulum, there is a continuous interchange between potential energy and kinetic energy. At the points of maximum displacement (the extremes of the swing), the pendulum momentarily stops, its velocity is zero, and all its energy is gravitational potential energy. As it swings towards the equilibrium position, potential energy is converted into kinetic energy, which is maximum at the equilibrium position where the velocity is also maximum. As it swings towards the other extreme, kinetic energy is converted back into potential energy. In an ideal undamped SHM, the total mechanical energy (the sum of potential and kinetic energy) remains constant.

6. What are damped oscillations, and how do they relate to a real-world pendulum?

Damped oscillations are oscillations where the amplitude of motion decreases over time due to energy loss, typically through frictional forces such as air resistance or friction at the suspension point. In a real-world pendulum, these damping forces are always present, causing the swings to gradually become smaller until the pendulum eventually comes to rest. Simulations often include a "damping" parameter that allows us to model and observe this reduction in amplitude.

7. What are forced oscillations and resonance, and can a pendulum exhibit these phenomena?

Forced oscillations occur when an external periodic force is applied to an oscillating system, causing it to oscillate at the frequency of the driving force. Resonance is a phenomenon that occurs when the driving frequency is close to the natural frequency of the system. At resonance, the amplitude of the forced oscillations can become very large. A pendulum can exhibit forced oscillations if it is periodically pushed or driven. If the frequency of this driving force matches the natural frequency of the pendulum, resonance can occur, leading to a significant increase in the amplitude of its swing, even with a small driving force.

8. How can simulations be used as a learning tool to understand pendulum motion and SHM?

Simulations provide a visual and interactive way to explore the abstract concepts of pendulum motion and SHM. They allow students to:

  • Visualize the motion and how different variables change over time through animations and graphs.
  • Investigate the effects of changing parameters (length, mass, gravity, damping, driving force) on the pendulum's behavior.
  • Collect and analyze data on period, frequency, amplitude, and energy transformations.
  • Test predictions and develop a deeper intuitive understanding of the underlying physics.
  • Explore different scenarios that might be difficult or impossible to set up in a physical lab (e.g., varying gravity or eliminating damping).
  • Connect theoretical concepts with observable phenomena through real-time feedback and multiple representations (e.g., motion, graphs, equations).
Details
Parent Category: 02 Newtonian Mechanics
Category: 09 Oscillations
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