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PHYSICS 8A-08 (03-18-10)

# PHYSICS 8A-08 (03-18-10) - PHYSICS 8A Professor Joel Fajans...

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PHYSICS 8A Professor Joel Fajans 3/18/10 Lecture 18 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 There is a short homework assignment due on Sunday the last day of spring break. LECTURE Today I will start a new topic. The question I would like to answer is: if I have a mass on the end of the spring and pull it out from the equilibrium position, it will bounce up and down at a frequency what is the frequency with which systems, such as this one, oscillate back and forth? I will start out with a horizontal spring mass system. As I mentioned to you, it is not possible to build this because we would need a frictionless surface, but the idea is that we have some mass resting on a frictionless surface attached to a spring with fce constant k , and the mass is displaced some distance x from its equilibrium position. I would like to know the subsequent motion. We can guess that it will oscillate back and forth, but let’s be a bit more concrete about what might actually happen. If we stretch this from the equilibrium position, there will be a force equal to kx as illustrated below. We write kx to remind ourselves that it points back toward equilibrium position. Let’s start out by drawing some graphs trying to guess what might happen. The first guess we might make is that if we stretch it out to some position, then it will head back toward the center, reach its maximum, and then go back the other way, oscillating back and forth. We guess a pattern: This pattern is not realistic because if we draw velocity as a function time, then velocity would be a square wave, as illustrated below, which would mean that the velocity is jumping from some negative value to a positive value without taking values in between. This is not physically possible. It is obvious from observing the pendulum that its speed changes gradually.

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PHYSICS 8A-08 (03-18-10) - PHYSICS 8A Professor Joel Fajans...

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