Mechanical impedance

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Mechanical impedance is a measure of how much a structure resists motion when subjected to a given force. It relates forces with velocities acting on a mechanical system. The mechanical impedance of a point on a structure is the ratio of the force applied to the point to the resulting velocity at that point.

Mechanical impedance is the inverse of mechanical admittance or mobility. The mechanical impedance is a function of the frequency ω of the applied force and can vary greatly over frequency. At resonance frequencies, the mechanical impedance will be lower, meaning less force is needed to cause a structure to move at a given velocity. The simplest example of this is when a child pushes another on a swing. For the greatest swing amplitude, the frequency of the pushes must be more-or-less at the resonant frequency of the system.

\mathbf{f}(\omega)=\mathbf{Z}(\omega)\mathbf{v}(\omega)

Where, \mathbf{f} is the force vector, \mathbf{v} is the velocity vector, \mathbf{Z} is the impedance matrix and ω is the frequency.

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