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Línea 13: |
| ==Ecuacion de Movimiento== | | ==Ecuacion de Movimiento== |
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| <math> -\propto\ddot{x}-kx+f_{0}cos\left( w_{0}t\right)=m\ddot{x} | | <math> -\propto\ddot{x}-kx+f_{0}cos\left( w_{0}t\right)=m\ddot{x} </math> |
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| \begin{document}
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| Sea A un sistema de masa m sujeto a un resorte ideal que obedece la Ley de Hooke y sea entonces por segunda ley de Newton obtenemos
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| \begin{center}
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| $-\propto\ddot{x}-kx+f_{0}cos\left( w_{0}t\right)=m\ddot{x} $
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| \end{center}
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| o bien
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| \begin{center}
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| $m\ddot{x}+\propto\dot{x}+kx=f_{0}cos\left( w_{0}t\right)$
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| \end{center}
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| Si definimos a $\beta\equiv\frac{\propto}{2m}$,$w\equiv\frac{k}{m}$ y $F_{0}\equiv\frac{f_{0}}{m} $ obtenemos la siguiente ecuacion diferencial
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| \begin{center}
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| $\ddot{x}+2\beta\ddot{x}+wx=F_{0}cos\left( w_{0}t\right)$.......(1)
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| \end{center}
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| cuya solucion general obtemos su sumar
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| \begin{center}
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| $ m\ddot{x}+\propto\dot{x}+kx=0 $
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| \end{center}
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| \begin{center}
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| $ Re\{\ddot{x}_{c}+2\beta\dot{x}_{c}+w^{0}x_{c}=F_{0}e^{iw_{0}t}\} $
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| \end{center}
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| \begin{center}
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| $x=e^{-\beta t}\{A_{+}e^{\sqrt{\beta^{2}-w_{0}^{2}}}+A_{-}e^{-\sqrt{\beta^{2}-w_{0}^{2}}}\}$
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| \end{center}
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| \begin{center}
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| $w_{1}^{2}\equiv w_{0}^{2}-\beta^{2}$
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| \end{center}
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| \begin{center}
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| Movimiento subamortiguado $(\beta^{2}-w_{0}^{2}<0)$
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| \end{center}
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| \begin{center}
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| Movimiento criticamente amortiguado $(\beta^{2}-w_{0}^{2}=0)$
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| \end{center}
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| \begin{center}
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| Movimiento sobreamortiguado $(\beta^{2}-w_{0}^{2}>0)$
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| \end{center}
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| \end{document}
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| </math>
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| ==El estado estable== | | ==El estado estable== |
Revisión del 00:32 3 mar 2009
Javier Ortiz Torres
Fenomenos Ondulatorios
javier19df@hotmail.com
--Introduccion 20:59 8 feb 2009 (CST)
Oscilaciones Forzadas
Introducción
Sistemas Forzados
Ecuacion de Movimiento
El estado estable
