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In books of dynamics, I normally see topics in kinematics and then in kinetics, and finally a last chapter on mechanical vibrations dealing with SDOF and MDOF systems. But I do not see any book mentioning how the topic of vibration fits in dyynamics? It feels natural to say to mechanical vibrations would be an extension of kinetics.

What is the correct classification of mechanical vibrations?

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"Kinetics" is just a synonym for "dynamics," and most English books use the term "dynamics" rather than "kinetics." There are plenty of mechanical engineering textbooks with "dynamics" in the title, but few with "kinetics" (I'm ignoring books on topics like "kinetics of chemical reactions", etc, which are not about mechanical engineering)

The difference between "kinetics" and "kinematics" is that kinematics deals with the motion of object without considering what causes that motion (for example the mathematical relationships between position, velocity, and acceleration of a particle moving along a given curved path in space), but kinetics/dynamics does consider the forces causing the motion (i.e. Newton's laws of motion).

Since a fundamental topic in studying mechanical vibrations is the fact that for linear elastic materials which obey Hooke's law, Newton's laws mean that the motion for small displacements about an equilibrium position is simple harmonic motion, I would classify most of the subject of "mechanical vibrations" to be part of dynamics/kinematics, rather than kinetics.

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  • $\begingroup$ What you say about SHM makes sense for linear systems as you point out. Is this why we have topics on kinematics of particles for which we say that rotation about mass centre is neglected? When we have a rigid body like a disc turning on a shaft and we write the equation of motion $J\ddot{\theta} + k\theta=0$, the disc is then assumed to consist of many particles but with each particle without any rotation about its own axis? Is this correct? $\endgroup$
    – user11206
    Commented Aug 21, 2018 at 9:14
  • $\begingroup$ @user11206 it is considered to be a more complex particle called a rigid body. Its sill just one mathematical thing. Everything is reduced to one point still. $\endgroup$
    – joojaa
    Commented Aug 21, 2018 at 15:32

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