About

1.7.4 The response of the oscillatory system depends on the value of the frequency of the periodic force (also known as the driving frequency).                LO (k)

When the driving frequency f  is close to or equal to the natural frequency f_o of the oscillating system, maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude.  This phenomenon is called resonance.      

 A more accurate and complicated picture could be found on Wikipedia.

 

This computer model can be used to generate a similar data representation when using the instruction found on the html below the model.

1.7.4.1 Case 1: b=0 no damping.

All 100 spring mass systems oscillates forever without coming to rest. Notice when the ratio of driving frequency to natural frequency f_o of the oscillating system  f/fo = 1  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (extended beyond 10).  This phenomenon is called resonance. 

  

1.7.4.2 Case 2: b=0.1 very light damping

Notice when the ratio of driving frequency to natural frequency f_o of the oscillating system  f/fo = 1  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (equal 10 m).  This phenomenon is called resonance. 

1.7.4.3 Case3: b=0.3 light damping

Notice when the ratio of driving frequency to natural frequency f_o of the oscillating system  f/fo slightly less than 1,  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (about 3.3).  This phenomenon is called resonance. 

1.7.4.4 Case4: b =0.6 moderate damping

Notice when the ratio of driving frequency to natural frequency f_o of the oscillating system  f/fo slightly less than 1 about 0.9 in this case,  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (about 1.8).  This phenomenon is called resonance.

1.7.4.5 Case5: b = 2.0 critical damping

Notice the resonance does not occur anymore. 

1.7.4.6 Case6: very heavy damping

Notice the resonance does not occur anymore. 

1.7.5 Model:

1. Run Sim
2. http://iwant2study.org/ospsg/index.php/88

1.7.6 YouTube explanation:

http://youtu.be/tl4hfZ3TR6U

1.7.7 YouTube

http://youtu.be/LV_UuzEznHs  How is this video related to resonance? Hint: consider the shaking support table is the driver, moving an driver frequency f, and the natural frequency of the left, middle and right structure each have their own natural frequency f₀₁, f₀₂, f₀₃.

http://youtu.be/17tqXgvCN0E This video shows the oscillating of a wine glass by playing sound (driver) at its(wine glass) natural frequency resulting in resonance.Note stroboscope is used to observe the resonant effect better.

http://youtu.be/M8ztJGT6AHc Marina Bay Sands cantilever - real world application of resonance.
Note that video ends at 5.40 min.

http://youtu.be/1yaqUI4b974 Though not really in A-Level Physics syllabus, the experiment shows the beauty of physics where sound at certain frequencies can produce detailed 2 dimensions patterns of sands that tends to be deposited at positions where the displacement is zero and areas of resonances (high amplitudes) the sand tend to be disturbed and move away from these position, resulting in the detailed patterns of sands.

 

Translations

Code	Language		Translator	Run

Credits

weelookang@gmail.com; leetatleong

Briefing Document: Student Learning Space Resonance Model

This briefing document summarizes the key concepts and functionalities of the "Student Learning Space Resonance type 1 HTML5 Applet Simulation Model" available on the Open Educational Resources / Open Source Physics @ Singapore website. This model is designed to help students understand the phenomenon of resonance in oscillatory systems.

Main Theme:

The primary focus is on demonstrating and explaining resonance, particularly how the driving frequency of a periodic force affects the amplitude of an oscillating system. The model illustrates that resonance occurs when the driving frequency is close to or equal to the natural frequency of the oscillating system.

Key Ideas and Facts:

• Resonance: The model demonstrates the phenomenon of resonance, defined as "maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude" when the driving frequency (f) is close to or equal to the natural frequency (f0).
• Driving Frequency vs. Natural Frequency: The simulation highlights the relationship between the driving frequency (the frequency of the external force) and the natural frequency (the inherent frequency of the oscillating system).
• Damping: The simulation explores the effect of damping on resonance. Different levels of damping (represented by the variable 'b') are modeled, showing how damping affects the amplitude at resonance and even eliminates resonance altogether.
• No damping (b=0): "All 100 spring mass systems oscillates forever without coming to rest...maximum amplitude (extended beyond 10)."
• Light damping (b=0.1, b=0.3): Resonance occurs, but the amplitude is limited. The peak of the resonance curve shifts slightly as damping increases.
• Moderate damping (b=0.6): Resonance is still observable, but with a significantly reduced amplitude.
• Critical and Heavy Damping (b=2.0 and very heavy): "Notice the resonance does not occur anymore."
• Maximum Energy Transfer: Resonance results in maximum energy transfer from the driver to the oscillating system.
• Simulation Functionality: The page provides a simulation model that allows users to experiment with different driving frequencies and damping coefficients.
• Real-World Examples: The page links to several YouTube videos illustrating resonance in real-world scenarios:
• A shaking support table causing different structures to resonate.
• A wine glass oscillating due to sound waves at its natural frequency.
• The Marina Bay Sands cantilever structure and its potential for resonance.
• Patterns created in sand by sound waves at specific frequencies.
• App availability: The resources includes a link to an app available on the Google Play Store: "https://play.google.com/store/apps/details?id=com.ionicframework.shm24app916792&hl=en"

Quotes:

• "When the driving frequency f is close to or equal to the natural frequency fo of the oscillating system, maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude. This phenomenon is called resonance."
• "Notice when the ratio of driving frequency to natural frequency fo of the oscillating system f/fo = 1 maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (extended beyond 10)." - (Case 1: b=0)
• "Notice the resonance does not occur anymore." - (Case 5: b = 2.0 critical damping, and Case 6: very heavy damping)

Educational Value:

This resource provides a valuable interactive tool for understanding resonance. The simulation allows students to visualize the relationship between driving frequency, natural frequency, damping, and amplitude. The included real-world examples help to contextualize the concept and demonstrate its relevance.

Resonance in Oscillatory Systems: A Study Guide

I. Key Concepts

• Oscillation: A repetitive variation, typically in time, of some measure about a central value or between two or more different states.
• Periodic Force (Driving Force): An external force that oscillates at a specific frequency and is applied to an oscillatory system.
• Driving Frequency (f): The frequency at which the periodic force oscillates.
• Natural Frequency (f₀): The inherent frequency at which an oscillatory system will vibrate when disturbed and left to itself.
• Resonance: A phenomenon that occurs when the driving frequency of a periodic force is close to or equal to the natural frequency of an oscillatory system, resulting in a maximum transfer of energy and a large amplitude of oscillation.
• Amplitude: The maximum displacement or extent of vibration from the equilibrium position.
• Damping (b): The dissipation of energy from an oscillating system, usually due to friction or other resistive forces, causing the amplitude of oscillation to decrease over time.
• Critical Damping: The level of damping that returns the system to equilibrium as quickly as possible without oscillating.
• Energy Transfer: The process by which energy is passed from the periodic force (driver) to the oscillating system.

II. Quiz

Answer the following questions in 2-3 sentences each:

1. What is resonance, and under what conditions does it occur in an oscillatory system?
2. How does the driving frequency relate to the natural frequency during resonance?
3. What is the effect of damping on the amplitude of oscillations?
4. In the context of resonance, what is the role of the periodic (driving) force?
5. According to the resource, what happens to the energy transfer between the driver and the oscillating system during resonance?
6. What happens to the amplitude of an oscillating system at resonance?
7. What is the significance of the damping coefficient 'b' in the simulations?
8. Explain how damping affects the resonance phenomenon.
9. Describe what happens in the simulation when the damping is very heavy.
10. Give one real-world example of resonance from the provided YouTube links, and briefly explain how it demonstrates the concept.

Quiz Answer Key

1. Resonance is a phenomenon where an oscillatory system vibrates with maximum amplitude when the driving frequency is near or equal to its natural frequency. This happens because energy is transferred efficiently from the driving force to the system.
2. During resonance, the driving frequency (f) is close to or equal to the natural frequency (f₀) of the oscillating system. This condition allows for maximum energy transfer and the largest possible amplitude.
3. Damping reduces the amplitude of oscillations over time by dissipating energy from the system. Higher damping leads to a faster decrease in amplitude and a reduction in the intensity of resonance.
4. The periodic force, or driver, is the external force that provides energy to the oscillatory system. It causes the system to oscillate, and its frequency determines whether resonance occurs.
5. During resonance, there is maximum energy transfer from the driving force to the oscillating system. This results in the system vibrating with its largest amplitude.
6. At resonance, the amplitude of the oscillating system is at its maximum. This is because the energy transfer from the driving force is most efficient when the driving frequency matches the natural frequency.
7. The damping coefficient 'b' represents the level of damping in the system. Higher values of 'b' indicate greater damping forces, which reduce the amplitude of oscillations and can suppress resonance.
8. Damping reduces the sharpness and intensity of resonance. With increased damping, the maximum amplitude at resonance decreases, and the resonance peak becomes broader.
9. With very heavy damping, resonance does not occur. The system quickly returns to equilibrium after being disturbed, with minimal or no oscillation.
10. The oscillating wine glass video demonstrates resonance when sound (the driver) is played at the wine glass's natural frequency. This causes the glass to vibrate intensely, potentially even shattering due to the large amplitude of oscillation.

III. Essay Questions

Consider the following essay questions:

1. Discuss the relationship between driving frequency, natural frequency, and damping in the phenomenon of resonance. How do these factors interact to determine the amplitude of oscillations?
2. Explain, with examples from the provided simulations and YouTube links, how resonance can be both a desirable and an undesirable phenomenon in real-world applications.
3. Describe the role of the computer simulation in understanding the concept of resonance. How does it aid in visualizing and analyzing the effects of different parameters on oscillatory systems?
4. Analyze the effect of varying the damping coefficient (b) on the behavior of the spring-mass system in the simulation. How does damping influence the transfer of energy and the amplitude of oscillations?
5. Compare and contrast the behavior of an undamped system (b=0) with a heavily damped system in the context of resonance. How does the absence or presence of damping affect the energy transfer and the system's response to a driving force?

IV. Glossary of Key Terms

• Oscillation: A repetitive back-and-forth motion around an equilibrium point.
• Periodic Force: An external force that varies in a repeating pattern over time, influencing an oscillatory system.
• Driving Frequency: The frequency at which the periodic force is applied to the system.
• Natural Frequency: The inherent frequency at which an object tends to oscillate when disturbed.
• Resonance: The condition where the driving frequency matches the natural frequency, leading to a maximum amplitude of oscillation.
• Amplitude: The maximum displacement of an object from its equilibrium position during oscillation.
• Damping: The reduction in amplitude of an oscillation due to energy dissipation.
• Critical Damping: The damping condition that allows a system to return to equilibrium in the shortest time without oscillating.
• Energy Transfer: The movement of energy from the driving force to the oscillating system, maximized during resonance.

 

 Apps

https://play.google.com/store/apps/details?id=com.ionicframework.shm24app916792&hl=en

iCTLT e-poster video 2 minutes

1. Version 30 March 2016 Minister
2. Version 17 March 2016   
3. Version 14 March 2016 
4. Version February  

iCTLT e-poster presentation

   https://docs.google.com/a/moe.gov.sg/presentation/d/10ejVJIyXA8u2DILcEbJ-RACLxoPvvqrTiC02fqfNJIc/edit?usp=sharing

 https://docs.google.com/presentation/d/1g7U7dwjxdQ8k9Z62AzXEQCM3K0NcNqvxCXugOXv-qpA/edit#slide=id.p4

 https://docs.google.com/presentation/d/1lSySjVaEDlIRBniKie2xyCu3B6go2AjJqe00D_vUr5Q/edit#slide=id.g10abfba361_0_25

 

Student Learning Space Resonance Applet FAQ

• What is resonance?
• Resonance is a phenomenon that occurs when an oscillating system is subjected to a periodic force (the driver) with a frequency close to or equal to the system's natural frequency. At resonance, energy is transferred efficiently from the driver to the oscillating system, causing it to vibrate with maximum amplitude. The driving frequency is denoted as f and the natural frequency is denoted as fo. Maximum energy transfer happens when f/fo=1.
• What is the "Student Learning Space Resonance type 1 HTML5 Applet Simulation Model"?
• It is a computer simulation model designed to demonstrate and explore the phenomenon of resonance in an oscillatory system, likely a mass-spring system. It is intended as an educational resource for physics students. The model allows users to observe how the amplitude of oscillations changes with varying driving frequencies and damping conditions.
• How does damping affect resonance?
• Damping reduces the amplitude of oscillations and alters the resonance effect. With light damping, resonance still occurs, but the maximum amplitude is smaller than in the undamped case, and the maximum amplitude occurs when f/fo is slightly less than 1. As damping increases, the maximum amplitude decreases. With critical or very heavy damping, resonance may not occur at all because energy is dissipated too quickly for a significant amplitude to build up.
• How can the simulation model be used for learning?
• The simulation model can be used to visually demonstrate the principles of resonance and how various factors, such as driving frequency and damping, affect the system's response. By experimenting with different parameters, students can develop a deeper understanding of the underlying physics and see how theoretical concepts translate into observable behavior.
• What are some real-world examples of resonance?
• The provided resources include links to YouTube videos illustrating real-world applications of resonance. Examples include the oscillating of a wine glass by playing sound, and the shaking support table moving with a driver frequency to induce resonance.
• What are the key parameters that can be controlled or observed in this simulation?

The key parameters are the driving frequency (f), the natural frequency of the oscillating system (fo), and the damping coefficient (b). The simulation allows you to observe how the amplitude of the oscillating system changes as you vary these parameters.

• Where can I find the simulation and related resources?
• The simulation itself can be accessed via the provided iframe embed code. The source also links to related YouTube videos and presentation materials that further explain the concept of resonance.
• Who developed this simulation, and what are the licensing terms for its use?

The simulation is part of the Open Educational Resources / Open Source Physics @ Singapore project. The licensing terms are Creative Commons Attribution-Share Alike 4.0 Singapore License, with a separate license for commercial use of the underlying EasyJavaScriptSimulations Library.