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E12: Linear Physical Systems Analysis
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 E12 : LINEAR PHYSICAL SYSTEMS ANALYSIS linear, lumped-parameter models, and similar fall 2002 spring 2004 - erik cheever

 Lab 1: Modeling Heat Transfer In this experiment we attempted to observe the similarities between thermal resistance and capacitance with their electrical counterparts (resistors and capacitors). This was accomplished by heating an enclosed insulated box with a light bulb, and measuring the temperature inside with respect to time. Comparing the results with what one would expect from an electrical circuit suggested that the thermal characteristics of the box indeed functioned and could potentially be modeled by an "equivalent" electrical circuit. E 11. Electrical Circuit Analysis An introduction to the analysis of electrical circuits that includes resistors, capacitors, inductors, op-amps, and diodes. The course aims to teach how to develop equations describing electrical networks. Techniques for the solution of differential equations resulting from linear circuits are taught. Solutions are formulated both in the time domain and in the frequency domain. There is a brief introduction to digital circuits. E 12. Linear Physical Systems Analysis Involves the study of engineering phenomena that may be represented by linear, lumped-parameter models. It builds on the mathematical techniques learned in E 11 and applies them to a broad range of linear systems including those in the mechanical, thermal, fluid, and electromechanical domains. Techniques used include Laplace Transforms, Fourier analysis, and Eigenvalue/Eigenvector methods. Both transfer function and state-space representations of systems are studied. The course includes a brief introduction to discrete time systems. Lab 2: Fighting Corrupt Speech In this lab we recorded a sample phrase with a 400 Hz noise behind it. We converted all the sample recordings into the frequency domain in order to make them easier to work with. We then used three different methods to try and filter out the noise, a subtraction method, a frequency threshold method and a frequency suppression method. Each of these methods worked pretty well but the frequency threshold method worked the best because it almost completely eliminated the noise without messing up the sample phrase. Lab 3: Double Trouble In this lab we tried to model the behavior of two coupled pendulums. We first experimented with an analytical system and then modeled the system in Simulink to verify our results from the first part. We showed that all possible motions of the two pendulums can be expressed by the combination of two functions which are the modes of the system. Lab 4: Speed Bump and Automotive Suspension Analysis The task of this experiment was to develop a model of a car going over a speed bump and to use the model to optimize the speed at witch the car went over that bump. The first simulation model was Model A where the car was given as a single mass and the shocks were composed of a spring and a damping element. The second simulation model was Model B where the car and shocks are modeled as in A but the tire is also modeled as a mass with a spring and damping element. Each of these models was tested on three different bumps modeled by cosine waves and on a discrete representation of a measured bump on the Swarthmore Campus. Three different car velocites were used to determine the responses to the various bumps by each suspension system model. Both automotive suspension models were simulated with Matlab's Simulink toolkit, but Model A was also simulated numerically with a Runge-Kutta differential equation solver method. Lab 5: The Human Transfer Function In this laboratory exercise, we modeled the human forearm with second-order linear time invariant differential equation methods. The 2nd order system's response to an initial offset condition was captured from real life by a computerized vision recognition system that tracked colored pieces of cloth attached at the elbow and the wrist. The experiment was repeated with the hand attached to the arm in question holding a 1.5 kilogram mass. The experimental data was also modeled theoretically with a Simulink analog computer approach. While the model used is a vast simplification of the complications of life, our model did more or less a decent job matching the real life data. final lab : Modeling Automotive Suspension with Analog Computing Methods A simple model of car suspension was simulated using an analog computer. The analog computer itself was first simulated on the computer with Multisim 7. Then, using discrete and integrated components, the analog simulator circuit was constructed on breadboards, and verified using a function generator to provide the road surface as input, and the output was observed using an oscilloscope. The results obtained clearly verify that the analog computer is a capable tool for accurate modeling of second order (and higher order) systems.

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