This lesson covers the fundamentals of vibration analysis of continuous systems. It delves into the techniques used for vibration analysis, the formulation of differential equations for discrete and continuous systems, and the application of Newton's law and D'Alembert's principle. The lesson also explains the concept of holonomic and non-holonomic systems, the use of equilibrium approach in problem formulation, and the importance of free body diagrams. It further illustrates these concepts with examples like a simple pendulum, a double pendulum, a rigid jointed plane frame, and a unicyclist moving along a curve. The lesson concludes with the discussion of phase plane diagrams and the solution of numerical problems related to natural frequencies.

- Vibration analysis of continuous systems involves the formulation of differential equations using various techniques.
- Newton's law and D'Alembert's principle are fundamental to this process.
- Holonomic systems have constraints that are functions of coordinates, while non-holonomic systems have constraints involving the derivatives of coordinates.
- Free body diagrams are essential in formulating problems and applying Newton's law.
- Phase plane diagrams are useful in representing the state of a dynamic system.

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