TRANSDUCERS 



voltage, for displacement charge, while the three components, mass, resis- 

 tance and compliance become inductance, resistance and capacitance. Were 

 this the final step there would be little point in the technique, as we should 

 have the same differential equation to solve with different symbols. However, 

 the fact that the equivalent equations can be set up means that the techniques 

 of Chapters 3, 4 and 5 (vector diagrams and the use of the operator j) 

 become available for the solution of mechanical problems. Any mechanical 

 'circuit' can now be drawn as an equivalent electrical circuit. The relation- 

 ship between the forces and displacements in the parts of the mechanical 

 circuit are exactly similar to the relationship between voltages and charges in 

 the corresponding electrical circuit. 



It is not usual in electrical circuit analysis to evaluate charge: its rate of 

 change with time, the current, is more commonly derived: 



I = 



dq 



At 



The solution of the electrical equivalent circuit will then give not displace- 

 ment, but velocity: 



d^: 



y = -7- 



dt 



Failure to realize this is the first common pitfall of electromechanical 

 analysis; in biological work the displacement is likely to be of greatest 

 interest, and must be derived from the equation 



X 



Jyd/ 



The second pitfall may occur in the transformation of a mechanical circuit 

 into an equivalent electrical one; it is often not self-evident whether certain 

 components must appear in series or in parallel in the equivalent circuit. 

 For this there is a simple rule: mechanical components subjected to the 

 same force are equivalent to electrical components with the same voltage, 

 i.e. in parallel. Similarly m.echanical components experiencing the same 

 displacement or velocity appear in series in the equivalent circuit. 



So far linear translational motion only has been discussed. Similar 

 considerations apply to circular motion, and the equivalent quantities for 

 both types of motion are summarized in Table 1. 



TABLE 1 



As an example of the use of electrical equivalent circuits, the performance 

 of the force-recording apparatus of Figure 33.1 will be analysed. 



474 



