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Physics 321

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Physics 321. Hour 33 Coupled Oscillators I. x 1. x 1. x 2. k 2. k 3. k 1. Example I. Assume solutions of the form: Note that is the same in both equations! – This defines a “normal mode.” Then. Normal Modes. Eigenvalues are Eigenvectors describe motion of the normal modes

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Physics 321

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  1. Physics 321 Hour 33 Coupled Oscillators I

  2. x1 x1 x2 k2 k3 k1 Example I

  3. Assume solutions of the form: Note that is the same in both equations! – This defines a “normal mode.” Then Normal Modes

  4. Eigenvalues are • Eigenvectors describe motion of the normal modes • Normal coordinates (not very useful!) Normal Modes

  5. coupled oscillators.nb Example

  6. normal coords.nb Example

  7. Physics 321 Hour 34 Coupled Oscillators II

  8. x2 k2 m Example II k1 M x1

  9. coupled carts.nb Example

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