lecture_10

lecture_10 - Lecture 10 0.1 Accelerometer The story we...

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0.1 Accelerometer The story we talked about last time was that of vertical support motion, the kind that occurs in earthquakes. Typical highest natural frequency of building motion is 1/10th of a Hertz, so short-duration earthquakes typically do not cause any trouble. It is the long-lasting ones, whose duration is many times the smallest period of oscillation of the building, that are the dangerous ones. In other words, in the limit of large ω/ω n , we had Z Y 1 p 1 + (2 ζ ) 2 and thus the oscillations of the building are damped, provided that ζ is large enough. There is another use for the formulas we have devel- oped last time, and that is when we want to measure position of the mass provided we are given the acceleration input. Why in the world would we want to do this? Just ask Nintendo. ..Of course, the Wii controller, shown in figure (1) contains a microelectromechanical sys- tems (MEMS)-based three-axis accelerometer. The game is supposed to make you move. I advise considering tennis, football, soccer and other outdoor activities. But the accelerometer works just fine. What enables it to measure acceleration is that we can see from the deriva- tions in the last lecture that for ω/ω n 0, i.e. for a very stiff system, the relationship between the position and driving acceleration becomes z ( t ) ≈ - 1 ω 2 n ¨ y. This is most easily seen by recalling the equation ¨ z + 2 ζω n ˙ z + ω 2 n z = - ¨ y = - ω 2 Y e iωt , observing our usual assumption z = | Z | e iωt - φ , differentiating and di- viding by ω 2 n . Now, MEMS accelerometers are usually designed so that the actual measurement is electronic: the mass sits between electrodes that are positioned in a ”comb”. The motion of the mass causes the change of the capacitance in the electrostatic comb, and this is recorded as the
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lecture_10 - Lecture 10 0.1 Accelerometer The story we...

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