CT-STEM

Forced Oscillations & Resonance

Forced Oscillations & Resonance

Subject: Physics,Engineering
Time: Students will need 1-2 class periods to use the simulation and perform the experiments, depending on the depth of discussion and detail the teacher is looking for.
Level: This is appropriate for high school physics classes studying any type of wave phenomena (such as sound), properties of materials, or simple harmonic motion (grades 9-12).

Overview

This activity uses the PhET Resonance simulation, found at: http://phet.colorado.edu/sims/resonance/resonance_en.html. Students will study free springs or pendulums prior to this activity, where the meaning of ‘free’ is a hanging spring or pendulum that is simply started in oscillation, with no other external forces trying to change its oscillation (outside of air friction, which decreases the amplitude of the oscillation). Students will be able to vary a number of parameters within the simulation. These parameters are frequency and amplitude of the mechanical driver (like the person pushing a swing), the spring constant, mass attached to the spring, and the level of damping in the system. Students will also be able to have multiple springs in the simulation which will allow them to compare and contrast the effects of changing parameters. This computer simulation experiment will allow students to investigate what resonance means for oscillating springs. The experiment can be a true inquiry experience for students, since details about resonance are generally not well-known. Student Outcomes • Explain the conditions required for resonance. • Identify/explain the variables that affect the natural frequency of a mass-spring system. • Explain the distinction between the driving frequency and natural frequency of a resonator. • Explain the distinction between transient and steady-state behavior in a driven system. • Identify which variables affect the duration of the transient behavior. • Recognize the phase relationship between the driving frequency and the natural frequency, especially how the phase is different above and below resonance. • Give examples the application of real-world systems to which the understanding of resonance should be applied and explain why.

Preparation

The only setup needed for this activity is Internet accessibility and making sure the PhET simulation can run on that particular computer system.  The teacher may consider having a hanging spring, pendulum, or other oscillator as a physical demonstration to remind students of definitions of oscillation, amplitude, spring constant, damping, and frequency.

In addition, the teacher may want to do physical demonstrations of natural frequencies of objects.  This could include any stringed instrument or stretched rubber bands, and how length, thickness, and tension determine the sound when plucked; something like a flute or soda bottle and blowing across the opening; pendulums and how the length determines the frequency; hanging masses on springs of different spring constants; tuning forks; or rubbing a wine glass with wet fingers.

Prerequisites

Students should have studied free oscillations prior to trying this simulated experiment.  Ideally this would include oscillating hanging springs with masses attached, but could be swinging pendulums.  Students should know the basic definitions associated with oscillatory motion, such as frequency, amplitude, and damping. 

Background

Resonance is a phenomenon for oscillating objects where an external force is being applied to the object, causing forced oscillations.  This is similar to pushing someone on a swing.  The person on the swing can continue swinging by itself, under the influence of gravity, and it does so freely at a normal, natural frequency.  When a second person comes along and begins pushing on the swinging person.  There can be two different frequencies in this system, the natural frequency of the swinging person, fnat, and the ‘forced’ frequency at which the second person is pushing, fforced.  The result is the swinging person will now be forced to swing at the forced frequency.  But one other thing about this situation is that the person pushing on the swing will get tired and the swinging person will notice it is not going very high – this is not an efficient use of energy and is not much fun.

However, if the person pushing on the swing such that the he or she matches the natural frequency of the swing, then the pusher will discover he does not get very tired and the person on the swing notices she is going higher and higher.  When the pusher and the swinger are doing so in synch with each other, such that fnat = fforced, the system is in resonance.  This is where the efficiency is highest the swing gets to its greatest amplitude. 

Students generally will appreciate the swing analogy, as they learn this feature through trial and error from a young age.  Students also appreciate demonstrations of what we mean by natural frequency, so they can more easily distinguish that from a driving frequency.

Compatible With


mac

windows

laptops

chrome books

phones

tablets

What's Next?

Standards

Next Generation Science Standards
  • Physical Science
    • [HS-PS4] Waves and their Applications in Technologies for Information Transfer
  • Engineering, Technology, Applications of Science

Computational Thinking in STEM
  • Modeling and Simulation Practices
    • Assessing Computational Models
    • Using Computational Models to Understand a Concept
  • Data Practices
    • Analyzing Data
    • Collecting Data
    • Creating Data
    • Visualizing Data

Comments, Feedback, and Quesitons

Forced Oscillations & Resonance

Teacher Notes

This activity uses the PhET Resonance simulation, found at: http://phet.colorado.edu/sims/resonance/resonance_en.html.

This is set up to do computer experiments, where a variety of parameters can be changed.  These parameters are driving frequency, driving amplitude, mass attached to the spring, spring constant, damping factor (i.e. frictional forces), and number of springs attached to the oscillator.

Teachers will seriously want to consider discussing with the whole class what is meant by controlled experiments, and show a brief example with this simulation before students try it on their own.  Students can work individually or with a partner on this activity.

 

Resonance is not something that is normally taught in any detail in high school, and most students will not know any details about it.  Some may be familiar and come up with an example like a singer being able to break a wine glass if she sings the right pitched note. But if the teacher is looking for an inquiry lesson, this might be useful because of the lack of knowledge of the students, and therefore students will make the discovery of what resonance is and what it depends on.

It is highly recommended to do demonstrations of natural frequency with students prior to them doing this computer experiment.  This could include any stringed instrument or stretched rubber bands, and how length, thickness, and tension determine the sound when plucked; something like a flute or soda bottle and blowing across the opening; pendulums and how the length determines the frequency; hanging masses on springs of different spring constants; tuning forks; or rubbing a wine glass with wet fingers.  These are all popular examples used when studying something like sound or simple harmonic motion.

 

Pre-lab:

Because many students will not be familiar with resonance, teachers may want to show examples of resonance.  If the teacher does not sing, a video showing a singer breaking glass can be used, such as that shown on the MythBusters, http://www.youtube.com/watch?v=IZD8ffPwXRo.  There is the classic Tacoma bridge disaster that may be the most dramatic example of resonance, http://www.youtube.com/watch?v=j-zczJXSxnw.  Or if the teacher has two resonance boxes and tuning forks, this demonstration of resonance (http://www.youtube.com/watch?v=hiHOqMOJTH4) can be done in class. 

 

Teachers will need to tell students what to expect when doing this computer experiment in terms of observations and the time needed to do this experiment well.  Students will need to watch carefully and be patient, as the simulation is designed to be realistic in terms of transient behavior.  What this means is if the user makes a small change in one of the parameters, there is not an instantaneous change in the motion being observed.  Rather, it takes time for the simulation to respond, as a real physical system would do.  In this sense, this particular simulation is useful in showing how a scientist really does his or her work in the lab.

 

Teachers should also recommend to students to make changes to parameters one at a time.  Students will need to be systematic and do a whole series of controlled experiments, so they can identify any cause-effect relationships between each parameter and resonance of the system.  Again, this is useful to put the student in the role of researcher, where they must be patient and disciplined when doing a more complex experiment.  It is also useful to remind students to do multiple springs at a time, to more easily see how one variable can make a difference in the resulting motion when the springs are driven by the frequency generator. 

 

It is useful to actually do this in class if enough computers are available.  Many students are likely to have questions about this activity, both because the material is new and also because the process involved might be slower than what they are used to in labs.  For those students or lab groups who like to get data quickly in labs, this will force them to be more patient because the simulated springs will not make immediate changes in motion to some steady-state (instead, students need to watch the transient behavior and try to describe it in words). 

 

Assessment

The teacher can use any standard lab report rubric for assessing student work. 

There are also questions from the lab that can be given to students, either as clicker type questions or as a quiz.  These are provided as downloadable files at http://phet.colorado.edu/en/contributions/view/3445.

 

Additional Information

A number of examples of demonstrations and videos have been provided above, and there are many more examples of videos related to resonance one can find by searching on ‘resonance’ on YouTube.  Many students enjoy searching these and finding their favorites to share with the class.  There are also some other PhET simulations that are related to oscillations.

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