Example: Force Driving a Mass

Consider a force $f(t)$ driving a mass $m$ to produce a velocity $v(t)=\dot{x}(t)$ at the driving point. By Newton's 2nd law,

$$\begin{eqnarray*} f(t) &=& m\, \dot{v}(t) \;\longleftrightarrow\;F(s) = ms\,V(s)... ...\omega) &\isdef &\frac{F(j\omega)}{V(j\omega)} \;=\; j\,m\omega \end{eqnarray*}$$

where $\omega$ is frequency in radians per second