About

1.2.6 Example 

The diagram shows the displacement-time graph for a body performing simple harmonic motion. Suggest in terms of period T the following
(a)    range of time where the velocity and acceleration are in same direction.
(b)    range of time where the velocity and acceleration are in opposite directions

suggested answers

$\genfrac{}{}{0.1ex}{}{T}{4}<t<\genfrac{}{}{0.1ex}{}{T}{2}and\genfrac{}{}{0.1ex}{}{3T}{4}<t<T$

$0<t<\genfrac{}{}{0.1ex}{}{T}{4}and\genfrac{}{}{0.1ex}{}{T}{2}<t<\genfrac{}{}{0.1ex}{}{3T}{4}$

1.2.6.1 Solution:

1.2.6.2 Model:

1. Run Sim
2. http://iwant2study.org/ospsg/index.php/75

 

Translations

Code	Language		Translator	Run

Credits

This email address is being protected from spambots. You need JavaScript enabled to view it.

http://iwant2study.org/lookangejss/02_newtonianmechanics_8oscillations/ejss_model_SHM12/SHM12_Simulation.xhtml

Briefing Document: ⚛️"10.2.6 Example Spring (k=9 N/m) - Mass (m=1 kg) JavaScript HTML5 Applet Simulation Model"

1. Overview

This document describes an interactive, web-based simulation model of a simple harmonic motion (SHM) system. The specific example detailed uses a spring with a spring constant (k) of 9 N/m and a mass (m) of 1 kg. The model is implemented as a JavaScript HTML5 applet, making it accessible across various devices and operating systems. It is part of a larger collection of open educational resources focused on physics.

2. Key Themes and Concepts

• Simple Harmonic Motion (SHM): The core concept is the simulation of SHM, which is the oscillatory motion of a system when the restoring force is proportional to the displacement from equilibrium. This specific model explores the motion of a mass attached to a spring.
• Interactive Simulation: The primary delivery method for this concept is an interactive, web-based applet. This allows users to directly observe and manipulate the parameters and observe the resulting behavior.
• Open Educational Resources: The applet is part of a larger collection of Open Educational Resources (OER), indicating that it's designed to be freely available and modifiable for educational purposes.
• Accessibility: The model is designed to work on a wide range of platforms and devices including:
• Android/iOS (including handphones/Tablets/iPads)
• Windows/MacOSX/Linux (including Laptops/Desktops)
• ChromeBook Laptops

3. Important Ideas and Facts

• Specific Parameters: The simulation is based on a spring with k=9 N/m and a mass of m=1 kg. These specific parameters are used as an example to illustrate the principles of SHM.
• Displacement-Time Graph Analysis: The accompanying example problem focuses on analyzing the displacement-time graph of an SHM system. Students are asked to determine:
• (a) The time ranges where velocity and acceleration are in the same direction.
• (b) The time ranges where velocity and acceleration are in opposite directions.
• Suggested Answers (Time Range in Terms of T): The suggested answers provided use the concept of the Period (T) of the motion:
• (a) Same Direction: "T / 4 < t < T / 2 and 3 T / 4 < t < T"
• (b) Opposite Directions: "0 < t < T / 4 and T / 2 < t < 3 T / 4"
• Simulation Access: The simulation is embedded within the page via an iframe, using the URL: https://iwant2study.org/lookangejss/02_newtonianmechanics_8oscillations/ejss_model_SHM12/SHM12_Simulation.xhtml. This allows users to interact with the simulation directly on the webpage.
• Software: The simulations are made with Easy JavaScript Simulation (EJS).
• Navigation & Breadcrumbs: The page's navigation structure clearly indicates its position within the website:
• Home > Interactive Resources > Physics > 02 Newtonian Mechanics > 09 Oscillations > 10.2.5 Example Spring model...
• This suggests a hierarchical organization of resources.
• Related Resources: The page provides a list of related simulation models and resources, demonstrating a wide range of physics topics and related tools. These include:
• Other SHM models, pendulum simulations, escape velocity models, models related to gravity, Newton's cradle, etc. This indicates that the page is part of a larger set of simulations.
• Models covering topics such as mechanics, gravitation, waves, electromagnetism, and even some chemistry, math, and geography.

4. Quotes:

• "The diagram shows the displacement-time graph for a body performing simple harmonic motion. Suggest in terms of period T the following (a) range of time where the velocity and acceleration are in same direction. (b) range of time where the velocity and acceleration are in opposite directions" - This explains the problem the students are supposed to analyze.
• "T 4 < t < T 2 a n d 3 T 4 < t < T" - The suggested answer for the time when velocity and acceleration are in the same direction.
• "0 < t < T 4 a n d T 2 < t < 3 T 4" - The suggested answer for the time when velocity and acceleration are in opposite directions.

5. Intended Use

The resource appears designed for use in junior college (high school) physics education, particularly in the context of teaching Newtonian Mechanics and Oscillations. The interactive nature of the simulation and the specific problem it poses suggest an approach that fosters active learning and problem-solving skills.

6. Implications and Significance

• Practical Learning: The simulation allows students to visualize abstract concepts related to SHM, promoting a better understanding of the underlying principles.
• Flexibility: The availability across multiple platforms and OS's increases the usability of the resource and lowers barriers to access.
• Open Source Nature: The fact that it is an open source simulation means that it is adaptable, modifiable and can be improved upon by the community.
• Part of Broader Resource Library: The resource is one of many physics simulations provided by the project, suggesting a comprehensive approach to interactive science education.

7. Conclusion

This specific simulation of a spring-mass system undergoing SHM provides a valuable interactive resource for physics education. The provided example problem encourages critical thinking about the relationship between displacement, velocity, and acceleration in SHM, and the accessibility of the tool on different platforms makes it a broadly applicable educational tool. The simulation is just a small part of a much broader and richer suite of materials for physics and math education.

Simple Harmonic Motion Study Guide

Quiz

Instructions: Answer the following questions in 2-3 sentences each.

1. What is simple harmonic motion (SHM)?
2. In the context of SHM, what do the terms displacement, velocity, and acceleration refer to?
3. If a spring with spring constant k = 9 N/m has a mass of m = 1 kg attached to it, and is undergoing SHM, describe the forces acting on the mass.
4. According to the source, during which time period in a cycle of SHM are the velocity and acceleration in the same direction?
5. According to the source, during which time period in a cycle of SHM are the velocity and acceleration in opposite directions?
6. Explain the relationship between displacement and acceleration in SHM.
7. What is the significance of the displacement-time graph for a body in SHM?
8. How can simulations, like the one referenced in the source, aid in understanding SHM?
9. How does the period, T, of SHM relate to the motion's velocity and acceleration?
10. How might the concepts of SHM be applicable in contexts beyond a simple spring-mass system?

Quiz Answer Key

1. 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. This means that the object will oscillate back and forth around an equilibrium position.
2. In SHM, displacement refers to the distance of the object from its equilibrium position, velocity is the rate of change of the object's displacement, and acceleration is the rate of change of the object's velocity, which is always directed towards the equilibrium position.
3. The mass attached to the spring experiences a restoring force proportional to its displacement from the equilibrium point, and directed towards the equilibrium. This force causes the mass to accelerate, while gravity is neglected.
4. The velocity and acceleration are in the same direction during the time periods T/4 < t < T/2 and 3T/4 < t < T, when the oscillating object moves towards the equilibrium.
5. The velocity and acceleration are in opposite directions during the time periods 0 < t < T/4 and T/2 < t < 3T/4, when the oscillating object moves away from the equilibrium.
6. In SHM, acceleration is always proportional to and opposite in direction to the displacement. When the displacement is greatest the acceleration is also greatest but in the opposite direction.
7. A displacement-time graph for an object in SHM graphically displays the periodic motion and illustrates the amplitude and the period of the oscillations. Its shape can also indicate the phase of the motion.
8. Simulations can provide a visual and interactive way to explore the relationships between displacement, velocity, and acceleration in SHM, making the abstract concepts more tangible and intuitive to understand.
9. The period, T, defines the duration of one complete cycle in SHM. The values of both velocity and acceleration change throughout the cycle, with maximum and minimum values that occur at regular time intervals that are related to T.
10. Concepts of SHM can be applied to many real-world phenomena involving oscillatory movement such as the swinging of a pendulum, vibrations of a guitar string, or the back-and-forth motion of an air molecule during a sound wave.

Essay Questions

Instructions: Please answer the following questions in essay format.

1. Analyze the role of the restoring force in simple harmonic motion, explaining how it contributes to the oscillatory nature of the movement, and discuss the ways in which its magnitude changes over the cycle.
2. Using both the provided information and your knowledge of physics, describe how the relationships between displacement, velocity, and acceleration in SHM are essential to characterizing the motion.
3. Discuss the different variables that affect the period and amplitude of SHM, and how you might observe changes in these parameters by experimenting with the referenced simulation.
4. Evaluate the benefits of using interactive simulations, like the one cited in the source, to enhance the understanding of abstract physics concepts like SHM.
5. Compare and contrast simple harmonic motion to other types of oscillatory motion, explaining the unique characteristics of SHM.

Glossary of Key Terms

• Simple Harmonic Motion (SHM): A type of periodic motion where the restoring force is proportional to the displacement and acts in the opposite direction of the displacement.
• Displacement: The distance of an object from its equilibrium position, usually measured in meters.
• Velocity: The rate of change of an object's displacement, indicating its speed and direction.
• Acceleration: The rate of change of an object's velocity, a measure of how quickly its velocity is changing, and always directed toward the equilibrium point in SHM.
• Restoring Force: The force that acts to bring an object back to its equilibrium position, and which is proportional to the object's displacement in SHM.
• Equilibrium Position: The point where the net force on an object is zero; where the oscillating object sits at rest without external disturbances.
• Period (T): The time it takes for one complete cycle of motion to occur, measured in seconds.
• Spring Constant (k): A measure of a spring's stiffness, the higher the spring constant, the more force it takes to stretch or compress the spring.
• Amplitude: The maximum displacement of an object from its equilibrium position.
• Simulation: A digital model of a real-world system, used to explore its behavior and interactions.
• Oscillation: A repetitive back-and-forth motion around an equilibrium position.

Video

https://notebooklm.google.com/notebook/3b9a546a-2d27-44d6-84de-3ce74023c961/audio

 

Frequently Asked Questions About Simple Harmonic Motion and Interactive Simulations

1. What is Simple Harmonic Motion (SHM), and how is it demonstrated in the provided resources? 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. The provided resource demonstrates SHM through a spring-mass system. This is shown both through an interactive simulation allowing users to visualize motion, and by a graph of displacement vs. time. The resources also explore the relationship between position, velocity, and acceleration in SHM.
2. How can the provided interactive JavaScript HTML5 applet simulations be used for educational purposes? These applet simulations provide a hands-on, visual way to understand physics concepts, particularly in Newtonian mechanics, oscillations, and simple harmonic motion. They allow users to manipulate parameters, observe real-time changes in the motion and related graphs, and thus enhance conceptual understanding. The simulations can be used on various platforms like desktops, laptops, tablets, and smartphones, making them accessible for diverse learning environments. The simulations also incorporate features that could be used in guided inquiry.
3. How are velocity and acceleration related in Simple Harmonic Motion (SHM)? When are they in the same direction and when are they in opposite directions? In SHM, velocity and acceleration are not always in the same direction. Velocity indicates the direction of movement, while acceleration indicates the direction of the net force causing changes in velocity. The resource provided an answer to this question as a sample problem. Velocity and acceleration are in the same direction when the mass is moving towards the equilibrium position (during the first quarter of the motion and the third quarter). Conversely, velocity and acceleration are in opposite directions when the mass is moving away from the equilibrium position.
4. What is the significance of the displacement-time graph in understanding SHM? The displacement-time graph visually represents how the position of an object undergoing SHM changes over time. It’s a sinusoidal curve with the amplitude corresponding to the maximum displacement, and the period representing the time for one complete oscillation. It is key to understanding the relationship between position, velocity and acceleration. Analysis of this graph shows how the velocity and acceleration vary and provides evidence that these quantities change their direction.
5. What types of physics topics are covered by the simulations and resources referenced? The resources are quite diverse covering topics including Newtonian Mechanics (particularly oscillations and SHM), gravity and gravitational fields, energy and potential, wave phenomena (such as superposition and diffraction), electromagnetism, optics, and more. The resources include virtual labs, simulations, and interactive models, which extend their value. These resources show some focus on teaching with interactive and visual methods.
6. What is "EJS" and how is it utilized in these resources? "EJS" refers to Easy JavaScript Simulations, an authoring toolkit used to create the interactive simulations that feature in these resources. EJS is a tool that allows educators and developers to easily create dynamic simulations, which are used in turn to enhance the learning process by making complex concepts easier to visualize and interact with.
7. Are these resources open source? What are the implications of their licensing? Yes, the content is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License. This means that they are open source and can be freely shared, adapted, and reused as long as proper attribution is given and derivative works are licensed under the same terms. For commercial use of the EasyJavaScriptSimulations Library, users need to contact This email address is being protected from spambots. You need JavaScript enabled to view it. and adhere to their specific license.
8. What are some of the other interactive tools beyond physics discussed in the resources? Beyond physics, the platform offers tools for a wide variety of subjects including mathematics (3D shapes, vector addition), chemistry (electrolysis, ionic bonding), geography (urbanization trends), literacy (word blending), and even interactive games and quizzes. This shows the flexibility of the EJS platform and its wide application in education.