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EXAMPLES

#### 17.6.1 Mass-Spring-Damper Vibration

A mass-spring-damper system is shown in Figure 17.29 A mass-spring-damper example with a sinusoidal input.

Figure 17.29 A mass-spring-damper example

The residues for the partial fraction in Figure 17.29 A mass-spring-damper example are calculated and converted to a function of time in Figure 17.30 A mass-spring-damper example (continued). In this case the roots of the denominator are complex, so the result has a sinusoidal component.

Figure 17.30 A mass-spring-damper example (continued)

#### 17.6.2 Circuits

It is not necessary to develop a transfer functions for a system. The equation for the voltage divider is shown in Figure 17.31 A circuit example. Impedance values and the input voltage are converted to the s-domain and written in the equation. The resulting output function is manipulated into partial fraction form and the residues calculated. An inverse Laplace transform is used to convert the equation into a function of time using the tables.

Figure 17.31 A circuit example

Figure 17.32 A circuit example (continued)