Forced Oscillations & Resonance
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).
Lesson OverviewThis 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.
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.
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.
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.
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