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