Impedance Diagram for Force-Driven Series Mass-Spring

Impedance diagram for the force-driven, series arrangement of mass and spring

Viewing the circuit as a (frequency-dependent) resistor network, it is easy to write down, say, the Laplace transform of the force across the spring using the voltage divider formula:

$$F_k(s) \eqsp F_{\mbox{ext}}(s) \frac{R_k(s)}{R_m(s)+R_k(s)} \eqsp F_{\mbox{ext}}(s)\frac{k/m}{s^2+k/m}$$

We will discuss further equivalent-circuit and impedance-network models such as these, as well as ways to digitize them into digital-filter form