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Introduction and Purpose
This project is similar to Building an op-amp sensor in that you will construct an instrument that can carry out special tasks. You may have noticed that all of the projects this semester have had a strong Physics orientation - that is, the projects relied more heavily on the physics you were currently studying than on the topics in the other FC courses. In this final project, your knowledge of RC circuits from Physics will be an essential part, but the overall direction of the project will have a strong Calculus emphasis.
For the final project this term, your team will be expected to build an analog computer. In brief, the analog computer uses operational amplifiers to solve differential equations. Digital computers can be used to solve differential equations by approximating the derivatives as finite differences, and carrying out the solution of the resulting difference equations by Euler's Method, or some other strategy (as we did last semester in solving Newton's equations for the Bungee Omelet project and this semester for the cab control project). An analog computer solves differential equations by integrating the equations in a continuous real-time manner.
The goal of this project is to design and construct an analog computer to solve linear differential equations. You will build the computer on your breadboards using the 741 op amps and various resistors and capacitors; and you will demonstrate the operation of the computers by solving the differential equation that yields Newton's Law of Cooling.
An additional component to this final project is that it will be used, at least in part, in determining your final grades in English, Calculus, and Physics, as well as Engineering! The final report for this project must be delivered on a webpage, and the English teachers have already given to you a document describing how they will evaluate the webpage. The Calculus instructor will review the webpages and look to see how you have carried out the differential equation solution processes.
Your analog computer should be able to solve Newton's Law of Cooling. Building a different circuit for each differential equation you want to solve would be impractical. There are a variety of physics situations where would be appropriate to modify your existing computer to solve the differential equation.
The assignment for the physics portion is to write a description of any physical situations where modifying the existing computer would be an appropriate initial attempt at solving the differential equation. Be sure to include why you would attempt to use the analog computer to solve the differential equation in your explanation. You should not limit yourself to situations we have seen in class, but also use ones from your daily life.
Please discuss with the instructors in the other FIPE components the amount this work counts toward the final grade.
Background Information
The following link is a document that demonstrates how an opamp circuit can be used to solve the differential equation from Newton's law of cooling.
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