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Example 2 degree of freedom system. Two masses connected by springs to walls and to each other. We analytically find the natural frequencies of the system near equilibrium and corresponding normal m…
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Normal Modes of Mechanical Systems - Oscillations and Instabilities
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- 1 Give a brief introduction to finding normal modes from the potential energy surface of an N degree of freedom system, and the three types of modes mentioned above.
- 2 Example 2 degree of freedom system. Two masses connected by springs to walls and to each other. We analytically find the natural frequencies of the system near equilibrium and corresponding normal m…
- 3 General motion near equilibrium is made up of a sum of normal modes (via the superposition principle), which gives rise to Lissajous figures.
- 4 Geometric interpretation of the equations of motion near equilibrium in terms of a "force field" for the case of a positive-definite potential energy matrix. For the eigendirections, we have what lo…
- 5 Normal coordinates: Using the normal modes as new generalized coordinates for the Lagrangian dynamics. The dynamics in the normal modes becomes decoupled and we consider the interpretation of quasip…
- 6 Why find normal modes? Because if have a mechanical system which is "forced", that is, has some oscillatory driving force that has a forcing frequency close to a natural frequency, we can get a larg…
