= Mechanical dynamic mass
{title2=$M_{\rm dyn}(s)=F(s)/A(s)$}
<Mechanical dynamic mass> is the complex <force>-to-acceleration ratio $M_{\rm dyn}(s)=F(s)/A(s)$ for a stated mechanical excitation and response. It is the scalar reciprocal of <mechanical accelerance> where that response is nonzero. Its units are <kilograms>, but a supported structure need not have a real, positive or constant dynamic ratio. An <impedance head> supplies separate force and acceleration channels from which this response can be estimated.<Impedance Heads: Types 8000 and 8001 by Brüel and Kjær>[Printed p.2, point-mobility discussion and footnote defining dynamic mass and accelerance]{ref}
For $m\ddot x+c\dot x+kx=F$ with zero <initial conditions>,
$$
M_{\rm dyn}(s)=m+\frac c s+\frac k{s^2},\qquad M_{\rm dyn}(i\omega)=m-\frac k{\omega^2}-i\frac c\omega.
$$
Equivalently, <mechanical dynamic stiffness> equals $s^2M_{\rm dyn}$. A freely translating ideal <mass> gives $M_{\rm dyn}=m$; a <spring>-supported <mass> includes the elastic and dissipative terms. With $m=2\,\mathrm{kg}$, $k=200\,\mathrm{N/m}$ and $c=4\,\mathrm{N\,s/m}$, at $\omega=5\,\mathrm{rad/s}$ the result is $(-6-0.8i)\,\mathrm{kg}$. At $10\,\mathrm{rad/s}$ it is $-0.4i\,\mathrm{kg}$. The negative real part in the first case describes a restoring-force contribution relative to acceleration; it is not a negative quantity of material.
An <impedance-head mass correction> subtracts the effective moving mass below the force-sensing plane from the measured scalar dynamic ratio, provided that material shares the measured acceleration. This is a force-plane correction, not removal of the sensor's physical influence on the structure. At an <antiresonance>, a small response can produce a very large reciprocal ratio; dividing by a channel near its noise floor makes that estimate unreliable. With coupled measurement coordinates, exchanging complete force/acceleration descriptions requires a <matrix inverse>, rather than the reciprocal of each transfer entry.
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