Lab: Investigation of Resonance Using Computer Simulated Experiments
Purpose:
In this computer experiment, we will be investigating the meaning of resonance, and finding the factors/parameters that affect the vibrating motion of springs. In particular, students should address and understand the following points after doing this lab:
1. Describe what resonance means for a simple system of a mass on a spring.
2. Identify, through experimentation, cause and effect relationships that affect natural resonance of these systems.
3. Give examples of real-world systems to which the understanding of resonance should be applied and explain why.
Materials:
You will need a computer with Internet accessibility, and being able to run Java for the simulation.
Research Question:
What is resonance? What factors affect resonance?
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.
Procedure:
We will be using a PhET Simulation. It is set up so that the student can vary a number of parameters for a spring-mass system. These parameters are mass attached to the spring, the spring constant, the frequency of a driver that the spring is attached to, the amplitude of the driver, and the damping factor for the system. This can be considered air friction, and will cause energy to dissipate from the system. One other feature is to have multiple springs attached to the driver, so direct compare-contrast can be done.
You will need to run controlled experiments. This means keeping all values of parameters constant, while choosing only one parameter to vary. This allows you to see the effect of that one parameter on the vibrations of the system.
Note to student: You are not expected to know much about resonance. The challenge for you is to act like a real scientist and, purely from your observations and measurements with the computer experiment, determine the cause and effect of each parameter on the vibration of the spring, and try to find conditions where the system goes into resonance with the driver.
Design your own experiments using the tools provided in the simulation to systematically identify what affects the natural resonance for mass-spring systems. You may want to start with damping set very low.
Organize your experiments and findings in data tables and in written descriptions of what the effect of each parameter is on the oscillations of the mass-spring system. Be sure to keep track of and record values of those parameters you are keeping constant.
Recognize that when you slowly vary the values of each parameter, you will need to watch what happens over a period of time before making more changes in value. This is because the simulation will show transient behavior – it takes a period of time for the system to settle into some sort of constant motion, rather than instantaneously settling down. This is a realistic representation for how things really work.
Most importantly, specifically find conditions where the mass-spring system is in steady-state resonance with the driver.
Analysis Questions:
1. In your own words, what is resonance? Provide an example from everyday life.
2. Specifically for the mass-spring system in this computer experiment, what does resonance mean?
3. Make two drawings. One drawing should show ‘in phase’ resonance between the mass-spring and the driver, and the other drawing should show ‘out of phase’ resonance between the mass-spring and the driver.
4. Provide three sets of conditions where you found resonance between the mass-spring and the driver. For each example, state whether the mass-spring was in phase or out of phase with the driver.
5. Summarize the cause-effect relationship between the mass-spring system and each parameter, in terms of what effect each parameter has on the vibration of the mass-spring system. Include observations of both transient and steady-state behavior. Which parameters are most important to find resonance between the driver and the mass-spring system?
Think of this as you are helping a student who doesn’t have access to this simulation. Write what you would tell them what you learned in your use of the simulation including illustrations that could be helpful.
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