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Michael, Your thinking is not "off". In terms of simply solving an algebraic problem, you are correct. But now, step back and look at the problem a little bit differently. Let's assume you don't know anything about pendulums and want to perform an experiment in which you vary the pendulum length, L, the mass, and the starting position. You also have the ability to measure the period accurately. (You may do this by measuring one period, or taking the average of many periods). You would find that T^2 is directly proportional to the pendulum length, and completely independent of the mass or the starting position (as long as the starting position wasn't "too high"). You now have a simple device that can accurately measure time, and is quite easy to calibrate (adjust the length) and keeps accurate time even as the power "runs down". This type of understanding of mechanisms is what lead to the development of portable, accurate clocks, which revolutionized navigation in the 17th Century. One goal of this type of physics analysis and experimentation is to develop an understanding of unique relationships between phenomena, and convert it into a mathematical model, if possible. Even at this moment, researchers in nanotechnology are using this type of modeling to develop new sensors and devices. Solve a problem, then step back to try to understand what the solution means. Christopher M. Seaman Technical Specialist ALCOA Technical Center

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