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I.1 Introduction
This chapter presents basic theories of mechanical vibrations:

• Analytical Dynamics of Discrete Systems
• Undamped Vibrations of n-degree-of-freedom Systems
• Analytical Dynamics of Continuous Systems

I.2 Analytical Dynamics of Discrete Systems
I.2.1 Principle of virtual work for a particle
Dynamic equilibrium of a particle of mass m:
where u[SUB]i[/SUB]: displacement
X[SUB]i[/SUB]: component of force field X
Virtual displacement (arbitrary for t[SUB]1[/SUB] < t < t[SUB]2[/SUB]):