Simulation Diagrams

In high-level circuit simulation tools, block diagrams are often contructed such that each block contains a transfer-function description of the system in that block. As an example, a one-pole filter with transfer function $H(s) = g/(s+a)$ may appear in the diagram as ``$g/(s+a)$'' in the box, viz.,

$$\rightarrow\fbox{$\frac{g}{s+a}$}\rightarrow$$

For the series mass-spring-dashpot system, where the input is defined as the force applied to the mass, and the output is defined as the resulting mass velocity, the transfer function is

$$H(s) = \Gamma(s) = \frac{b_1 s}{s^2 + a_1 s + a_0}$$

where $b_1 = 1/m$, $a_1 = \mu/m$, and $a_0 = k/m$.