About

Mass spectrometry

This is the simulation of the motion of a mass m situated at the end of a spring of length l and negligible mass. The motion is restricted to the horizontal dimension. (We choose a coordinate system in the plane with origin at the fixed end of the spring and with the X axis along the direction of the spring).

We assume that the reaction of the spring to a displacement dx from the equilibrium point can be modeled using Hooke's Law, F(dx) = -k dx , where k is a constant which depends on the physical characteristics of the spring. Thus, applying Newton's Second Law, we obtain the following second-order ordinary differential equation:

where x is the horizontal position of the free end of the spring.

In the simulation we solve numerically this equation and visualize the results.

Activities

1. Measure the period of the motion for the given initial conditions.
2. Drag with the mouse the ball to a new position and measure the period again. What do you observe?
3. Set the mass of the ball to several different values (keeping k constant) and plot in your notebook the observed period versus the mass.
4. Do the same for the elastic constant of the spring, k.
5. Would you dare to provide an explicit formula for the dependence of the period with respect to the mass and k?
6. Should the total energy of the model be preserved?
7. Why do you think the total energy of the simulation slowly increases? (Hint: choose a better solver for the equations, such as Runge-Kutta, and check again.)

 

Translations

Code	Language		Translator	Run

Credits

Wolfgang Christian; Francisco Esquembre

Briefing Document: Mass Spectrometer JavaScript HTML5 Applet Simulation Model and Related Educational Resources

1. Overview

This document reviews the "Mass Spectrometer JavaScript HTML5 Applet Simulation Model" by Leong TK, hosted on the Open Educational Resources / Open Source Physics @ Singapore platform. This applet is part of a broader collection of interactive physics and math simulations designed for educational purposes. The primary focus is on a simulation of a mass on a spring, governed by Hooke's Law, but the broader context reveals a wealth of open-source resources for educators.

2. Key Themes and Ideas

• Interactive Simulation as a Learning Tool: The core of the resource is an interactive simulation of a mass-spring system, intended to help students understand concepts like Hooke's Law, simple harmonic motion, and the relationship between mass, spring constant, and period of oscillation. The document highlights the use of simulation as a tool for active and inquiry based learning.
• Open Source and Educational Focus: The platform is explicitly geared towards providing free and open-source resources for educational use. The use of the term "Open Educational Resources" and the Creative Commons license clearly indicate a commitment to sharing and adapting educational materials.
• JavaScript/HTML5 Implementation: The simulations are built using JavaScript and HTML5, making them accessible through web browsers without requiring special software. This facilitates ease of use and integration into online learning environments.
• Model of the Mass-Spring System: The simulation models the motion of a mass m attached to a spring with a spring constant k and initial length l. The force acting on the mass is described by Hooke's Law: F(dx) = -k dx. The resulting motion is governed by the second-order differential equation: d²x/dt² = -k/m (x-l).
• Exploration and Experimentation: The simulation activities encourage students to investigate the system's behavior by:
• Measuring the period of motion under various initial conditions.
• Dragging the mass to new positions and observing changes in motion.
• Varying the mass m and the spring constant k to analyze their impact on the period.
• Attempting to derive a mathematical formula for the period's dependence on m and k.
• Considering the conservation of energy in the model.
• Broader Collection of Resources: The "Mass Spectrometer" simulation is just one element in a much larger library of simulations covering various topics in physics, mathematics, and chemistry. This broad scope allows users to access multiple learning tools within a consistent framework.

3. Important Facts and Quotes

• Hooke's Law: The simulation utilizes Hooke's Law, "F(dx) = -k dx", to model the spring's behavior, which states the restoring force of the spring is directly proportional to the displacement from its equilibrium position.
• Newton's Second Law: The motion of the mass is described by "Newton's Second Law," leading to the equation: "d2x / dt2 = -k/m (x-l)", where x is the horizontal position of the mass, and this forms the basis of the numerical simulation.
• Simulation Activities: The suggested activites are designed to help students learn experientially. For example:
• "Measure the period of the motion for the given initial conditions."
• "Drag with the mouse the ball to a new position and measure the period again. What do you observe?"
• "Set the mass of the ball to several different values (keeping k constant) and plot in your notebook the observed period versus the mass."
• Numerically Solved: "In the simulation we solve numerically this equation and visualize the results."
• Emphasis on Inquiry: Students are asked to "Would you dare to provide an explicit formula for the dependence of the period with respect to the mass and k?" showing the emphasis on getting students to actively investigate the math and physics being modeled.

4. Additional Insights from the Wider Context

• Diversity of Simulation Topics: The listed resources indicate a very wide range of topics covered, from basic mechanics (projectile motion, pendulums) and electromagnetism (magnetic fields, Lorentz force) to math concepts (fractions, geometry) and chemistry (titrations, radioactive decay).
• Use of Tracker: Many resources involve "Tracker," suggesting the use of video analysis to study real-world phenomena and then build models. For example, many of the listed sources have the phrase "Tracker" as a prefix to the simulation title.
• Open Source Tooling: The frequent mentions of "Easy Java Simulation" (EJS) or "EJSS" highlight the importance of this specific tool in the creation of these simulations. This is a clear connection to the development and use of open-source software in educational contexts.
• Collaborative Development: The credits mention multiple developers, such as Wolfgang Christian and Francisco Esquembre, indicating a collaborative approach to developing the open educational resources.
• Awards & Recognition: There are many mentions of awards in this document, indicating high quality and commitment to excellence. For example, one section notes "🏆2015-6 UNESCO King Hamad Bin Isa Al-Khalifa Prize for the Use of ICTs in Education".
• Ongoing Development and Updates: The existence of multiple versions and continued workshops (e.g., "20250113 Using SLS Authoring Co-Pilot and DeepSeek AI to Generate Quizzes") suggest a continued effort in refining and expanding the resource collection.

5. Conclusion

The "Mass Spectrometer JavaScript HTML5 Applet Simulation Model" is a valuable educational tool. The resource itself is embedded within a well-established ecosystem of open-source physics and math simulations that appear to be widely used in Singapore. The platform strongly encourages interactive learning, exploration, and the active development of mathematical and scientific understanding. The sheer volume of simulations and resources points to a dedicated community committed to improving teaching and learning through these kinds of methods.

 

Mass Spectrometer Simulation Study Guide

Quiz

1. What physical system does this simulation model?
2. What is the primary force acting on the mass in the simulation?
3. What does k represent in the simulation's equation?
4. What does m represent in the simulation’s equation?
5. What type of differential equation describes the motion?
6. What does the simulation numerically solve in order to visualize the motion?
7. What does the simulation ask the user to measure regarding the motion of the mass?
8. How does changing the mass affect the period of motion?
9. How does changing the elastic constant (k) affect the period of motion?
10. Why does the total energy of the simulation slowly increase over time?

Quiz Answer Key

1. The simulation models the motion of a mass attached to the end of a spring, restricted to horizontal movement.
2. The primary force acting on the mass is the restoring force of the spring, described by Hooke’s Law.
3. k represents the elastic constant of the spring, which determines its stiffness or resistance to deformation.
4. m represents the mass of the object attached to the spring.
5. The motion is described by a second-order ordinary differential equation.
6. The simulation numerically solves the second-order differential equation to determine the position of the mass over time.
7. The simulation asks the user to measure the period of the motion, the time it takes for the mass to complete one full oscillation.
8. Increasing the mass of the object will increase the period of motion.
9. Increasing the elastic constant (k) of the spring will decrease the period of motion.
10. The total energy of the simulation slowly increases over time due to the numerical solver used, which can introduce inaccuracies; a Runge-Kutta solver would improve the results.

Essay Questions

1. Discuss the relationship between Hooke's Law, Newton's Second Law, and the differential equation used in the simulation. How do these fundamental laws of physics contribute to the model of the mass-spring system?
2. Explain how the simulation demonstrates the concept of simple harmonic motion (SHM). What conditions must be met for a system to exhibit SHM, and how are those conditions represented in the model?
3. Analyze the activities proposed in the simulation. What specific learning outcomes are intended through each activity, and how do they support a deeper understanding of mass-spring systems?
4. Evaluate the limitations of this simulation as a model of a real-world mass-spring system. What simplifying assumptions are made, and how might these affect the accuracy of the simulation?
5. If you were tasked to improve this simulation, what additions or changes would you make? What would your additions do to help increase the accuracy and educational value of the simulation?

Glossary of Key Terms

Mass (m): The quantity of matter in an object; in this context, it refers to the mass of the object attached to the spring. Elastic Constant (k): A measure of the stiffness of a spring; a higher value indicates a stiffer spring, also called spring constant. Hooke's Law: A law stating that the force needed to extend or compress a spring by some distance is proportional to that distance; expressed as F = -kx, where x is the displacement from equilibrium. Newton's Second Law: A law stating that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass; expressed as F = ma. Differential Equation: An equation that relates a function to its derivatives; in this simulation, it is used to describe the motion of the mass-spring system. Second-Order Ordinary Differential Equation: A differential equation that involves the second derivative of an unknown function with respect to one independent variable. Numerical Solver: A method used to approximate the solution of a differential equation when an exact analytical solution is not available. Period (T): The time it takes for an oscillating system to complete one full cycle of motion; measured in seconds. Simple Harmonic Motion (SHM): A type of oscillatory motion in which the restoring force is directly proportional to the displacement, resulting in periodic oscillations. Runge-Kutta Method: A family of numerical methods for solving ordinary differential equations that provides more accurate results than some simpler methods.

 Version:

1. http://opensourcephysicssg.blogspot.sg/2017/10/mass-spectrometer-javascript-html5.html

Other Resources

[text]

Frequently Asked Questions about the Mass Spectrometer Simulation

• What does the Mass Spectrometer JavaScript HTML5 applet simulate?
• This applet simulates the motion of a mass attached to a spring, constrained to move in one horizontal dimension. It models the spring's behavior using Hooke's Law, where the restoring force is proportional to the displacement from the equilibrium position. The simulation numerically solves the second-order differential equation derived from Newton's Second Law, which describes this motion, and provides a visual representation of the mass's movement. Note this simulation is not actually a mass spectrometer, but shares some of the same physics.
• How can I interact with the simulation?
• Users can interact with the simulation in several ways: by dragging the mass to new initial positions, changing the mass of the ball, and adjusting the spring's elastic constant. The applet allows you to measure the period of oscillation with different parameters set.
• What is Hooke's Law, and how is it used in this simulation?
• Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from its equilibrium length. In the simulation, this is represented as F(dx) = -k dx, where F is the force, dx is the displacement, and k is the spring constant, a measure of the spring's stiffness. The negative sign indicates that the force is a restoring force, always acting to return the spring to its equilibrium position. This force is a crucial component in modelling the mass's motion.
• What is the relationship between the period of oscillation and the mass and spring constant?
• The simulation allows users to investigate this relationship by measuring the period of motion while systematically varying the mass of the ball and the elastic constant of the spring. By plotting the observed period against mass (keeping k constant) and the period against k (keeping mass constant), the user can observe how the two factors independently affect the period. The simulation does not provide the explicit formula, leaving that as an exercise for the user to try to derive, but it demonstrates that the period increases with increasing mass and decreases with increasing spring constant.
• Is the total energy of the system preserved in the simulation?

Ideally, in a closed system, the total energy, i.e. the sum of kinetic and potential energies, should be preserved. However, in this particular simulation, the energy slowly increases over time. This is due to the limitations of the numerical solver being used. The activity page hints that using a more precise solver, such as Runge-Kutta, can greatly improve the energy conservation of the simulation.

• Why does the simulation energy slowly increase, and what can be done to correct this?
• The energy increase is an artifact of the numerical method used to solve the equations of motion. The solver introduces small errors at each time step, which can accumulate over time and lead to a gradual increase in total energy. Using a higher-order numerical solver such as the Runge-Kutta method, can significantly minimize these errors and improve the simulation’s energy conservation properties.
• What other resources are available from this organization?
• The simulation is hosted on a site that provides many other interactive physics, chemistry, and mathematics applets for learning. This includes simulations of projectile motion, electric fields, magnetic fields, wave behavior, and even mathematical games. Many of the resources focus on open-source learning tools and interactive simulations to help better understand physical and mathematical concepts.
• Can I use or embed this simulation in my own webpage?
• Yes, the source code and simulation are offered under a Creative Commons license, implying it can be shared and adapted. The page provides embed code to allow users to add this simulation directly to any web page. However, you should note that commercial use of the simulation might require contacting the original authors and adhering to additional licensing guidelines.