PS11 - 4. Find the normal mode eigenfrequencies. Is the...

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Phys601/F11/Problem Set 11 Due Dec 5, 2011 To be upgraded 11.1H Normal modes A particle of mass m and charge q is connected to the origin by a spring of constant m ω 0 2 . Crossed E and B fields are externally applied. E = E 0 x ^ and B = B 0 z ^ , where E 0 and B 0 are constants. 1. Write down the Lagrangian for the system assuming the motion is in the 2D x-y plane only. 2. Find a static equilibrium. What are the balancing forces for this? 3. Obtain the equations for small oscillations about this equilibrium.
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Unformatted text preview: 4. Find the normal mode eigenfrequencies. Is the system stable? 5. What is the effect of E on your normal modes. 6. What are the approximate eigenfrequencies for B 0 and B . Keep corrections up to the first non-vanishing order. Comment. 11.1G Rotating Frames Goldstein Ch4 Problem 4.24 11.1Q Normal modes...
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This note was uploaded on 12/29/2011 for the course PHYSICS 601 taught by Professor Hassam during the Fall '11 term at Maryland.

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PS11 - 4. Find the normal mode eigenfrequencies. Is the...

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