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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Part 2 Symmetry and Invariance 4. Symmetry 21 5. Proportional reasoning 26 6. Box models and conservation 40 7. Dimensions 48 The first part of this book discussed how to organize, and therefore how to manage com- plexity. The second and third parts discuss how to eliminate complexity , with this second part discussing three methods for finding and removing complexity that is not real. The three methods are proportional reasoning, conservation, and dimensional analysis, and are examples of symmetry reasoning. Symmetry is also a powerful technique on its own, even without using its for the three methods. The next chapter therefore presents general examples of symmetry reasoning, and the following chapters develop this method reasoning into the three methods of proportional reasoning, conservation, and dimensional analysis. | {z } 23 4 Symmetry j A ( max ) = = jQ . 1 / Q The factor of Q in the maximum response says that a lightly damped system, where Q 1 , can reach a high amplitude if you push it at the so-called resonant frequency. The j says that the response at this resonant frequency lags the input by 90 degrees. In other words, that the response at this resonant frequency lags the input by 90 degrees....
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feb20b - MIT OpenCourseWare http://ocw.mit.edu 6.055J /...

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