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Figure 2: Idealization: spring and
damper
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Figure 1: Spring-steel cantilever and damping air-pot.
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In this lab, the time response of a first-order system is demonstrated. This system consists of a spring and a damper, respectively represented by a cantilever and an air dashpot (figure 1). The cantilever is made of spring-steel and can be modeled as a linear spring, i.e. the force at the tip of the cantilever is linearly dependent on its displacement. The dashpot can be modeled as a pure damper where the damping force is proportional to velocity as long as the volume of air behind the piston is not too large. The mass of the cantilever can be neglected, as long as the damping of the air dashpot is not too small. Students will observe that the system departs significantly from these idealizations in some circumstances. This nonideal behavior can be the motivation for postulating more complex models. A schematic representation of the system is shown in figure 2.
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Figure 4: A simple camera records the data
as an animation on the screen.
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Figure 3: Air dashpot without
rubber coating
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The glass dashpot is covered with rubber to protect the user if it breaks. In figure 3, the dashpot without the rubber coating is displayed, showing the plunger and the adjustment wheel. This wheel adjusts the damping by changing the opening through which air flows. Figure 4 shows a simple 'webcam' that records the data as video. The recording software lets you configure the frame rate. By looking at the individual frames of the animation, a table of position and time can be constructed. The data can then be processed into a plot that can be used to deduce the time constant tau (figure 5).
Why video data acquisition? In the first several labs, our goal is to have dynamics which are on a time scale to be directly observable by the students, both visually and through tactile sensations. Recording the data as video frames bypasses any more abstract instrumentation to present the dynamics in a form where motions are clear. An advantage of video acquisition is that the student can single step through the frames which are recorded 20 per second. Thereby, the motion is frozen down into sufficiently fine steps that numerical data can be acquired.To see an example of such a video capture click on the video button:
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Figure 5: Response of a first order system to an initial displacement.
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Each lab has an associated prelab assignment with the purpose of introducing the theory of the upcoming lab session to the students. By reading the prelab and answering the questions, the students will be able to understand the actual lab session better and spend less time on trivial problems. During the lab session, a lab questionnaire guides the students to reach the goals of that lab.
See below for examples of prelab and lab assignments:
Prelab1.pdf
Lab1.pdf
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