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An analogy with electrical circuits can be very useful when analyzing mechanical systems. A commonly used analogy, though not a unique one, is to relate mechanical and electrical quantities, as shown in Table 2-2.

TABLE 2-2 Torque–Current Analogy

Mechanical system	Electrical system
Torque (T)	Current (i)
Angular speed (ωm)	Voltage (v)
Angular displacement (θ)	Flux linkage (ψ)
Moment of inertia (J)	Capacitance (C)
Spring constant (K)	1/Inductance (1/L)
Damping coefficient (B)	1/Resistance (1/R)
Coupling ratio (nM/nL)	Transformer ratio (nL/nM)

The coupling ratio is discussed later in this chapter.

For the mechanical system shown in Fig. 2-11, Fig. 2-12a shows the electrical analogy, where each inertia is represented by a capacitor from its node to a reference (ground) node. In this circuit, we can write equations similar to Eqs. (2-31) through (2-33). Assuming that the shaft is of infinite stiffness, the inductance representing it becomes zero, and the resulting circuit is shown in Fig. 2-12b, where ω_m = ω_M = ω_L. The two capacitors representing the two inertias can now be combined to result in a single equation similar to Eq. (2-23).