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Advanced Physics Homework Help
Solving for Normal Modes in a Non Similar Coupled Pendulum
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[QUOTE="TSny, post: 4534661, member: 229090"] It's essentially part of the definition of "normal mode" that each particle has the same frequency. See: [url]http://en.wikipedia.org/wiki/Normal_mode[/url]. Also, in a normal mode, the particles move either "in phase" with each other or "out of phase" with each other. This mean that you can assume that the phase constant ##\phi## is the same for each particle. "Out of phase" then means that A[SUB]1[/SUB] and A[SUB]2[/SUB] will have opposite signs. In finding the normal modes, you can actually just let ##\phi = 0##. So, you can make the assumption that the motion of each particle is described by x[SUB]1[/SUB]=A[SUB]1[/SUB]cos([itex]\omega[/itex]t) x[SUB]2[/SUB]=A[SUB]2[/SUB]cos([itex]\omega[/itex]t) If you sub these into your two equations of motion, you will be able to determine the possible normal mode frequencies and whether the particles move in phase or out of phase in each mode. [EDIT: You can explore the normal modes of a similar system here: [url]http://www.falstad.com/coupled/[/url] You can change to 2 masses and you can vary the individual masses (click on "mouse:pull string"). You can select either normal mode or a combination of the modes (slide the two dots near the middle left side of the screen).] [/QUOTE]
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Solving for Normal Modes in a Non Similar Coupled Pendulum
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