Final Project for E12: Phyiscal Systems Analysis II
Prepared by Caleb Shetland, Johanna Yoon, Kam Woods,
David Knouf, and Stefan Gary
Introduction
For any mechanical system, an analogous electrical system may be constructed. An electrical system is often easier to build correctly, test precisely, and store compactly; this is the motivation behind the use of an analog computer, which is a system that outputs an analog voltage corresponding to some mechanical quantity to be examined, such as displacement. In this experiment, an analog computer was designed to model a system consisting of two loosely-coupled pendula. The circuit was constructed such that the two output voltages correspond to the angular displacement of the two pendula; setting one of these points to a certain voltage and then disconnecting it is equivalent to drawing one of the pendula aside and releasing it. The output voltages are sent to the analog input channels of a computer’s data acquisition board; these two channels are sampled at 30 Hz and are used to animate two pendula onscreen.
Conclusion
In comparing the analog computer output to the expected output from a
digital computer simulation, it is shown that an analog computer can be an
effective way to model a system. The computer is very difficult to
tune so that its output completely matches expected output due to the
large number of components and complicated circuit structure. In
addition, non-linear effects from the components can affect the operation
of the analog computer as well as the possibility of components with
inaccurate values. Despite the difficulties involved with modeling, the
analog computer performed well and ended up matching the general trends
predicted by the digital computer simulation.
Analog computers are extremely interesting and instructional systems. As
a laboratory group, we each gained much more familiarity with operational
amplifier circuits and also deeply enjoyed the process of building,
testing and analyzing the results.