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PHYSICS 8A-08 (03-30-10)

PHYSICS 8A-08 (03-30-10) - PHYSICS 8A Professor Joel Fajans...

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PHYSICS 8A Professor Joel Fajans 3/30/10 Lecture 19 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy, or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS We have a midterm next week! I haven’t figured out what’s on it yet. It may or may not cover the material we’re covering now but it will certainly cover up to oscillations. It will not be cumulative in the sense that I will not have 1D kinematics on the exam, but you will need to remember the stuff we’ve done from the beginning. I haven’t decided whether or not you will be allowed a cheat sheet. I hope to write the midterm tomorrow, so I will be able to give you more information Thursday. There is likely to be a short problem set due this weekend. LECTURE When we left, we were talking about damped oscillations. In other words, if I start a spring mass oscillation going, it goes for some time. If I put damping into the system, something that introduces friction, the oscillations go away. We used the term “damp out.” We talked about different sorts of damping. There are a couple different regimes people talk about when discussing damping. Underdamped : the size of the oscillations decreases exponentially. The formula characterizing this is ݁ ିఊ௧ . You do not need to know the mathematics behind this. If we increase the damping enough, you don’t get any oscillations at all. If you work out the math, this is another exponential. This is the overdamped case. The La Brea tar pits have vats of tar and pistons you can push on. This is a very overdamped system: if you put a spring on there, the spring would eventually get the system to come back to equilibrium position, but it would take forever because it takes an enormous amount of time to drive something through the tar. Critical damping is when you take an overdamped system and reduce the damping until you have the minimum amount of damping, but the system doesn’t oscillate. If you went further you would see oscillations.
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PHYSICS 8A ASUC Lecture Notes Online: Approved by the UC Board of Regents 3/30/10 D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. 2 What is the condition for a door? You want it to close in the minimum amount of time. On the other hand, you don’t want the door to oscillate. You want it to come and close with very little velocity. It turns out that door closers are made so that they are critically damped. They have a spring in them and a damper, and the critical damping ensures the door closes as quickly as possible, but closes with zero velocity. The shocks in your car are also critically damped.
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PHYSICS 8A-08 (03-30-10) - PHYSICS 8A Professor Joel Fajans...

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