MECHANICAL PROPERTIES OF TRANSDUCERS 



directly to evaluate the performance of a mechanical device, whether its 

 final output be mechanical or electrical. 



Electrical circuits are compounded of three principal components: induc- 

 tance, resistance and capacitance. In a similar way, we may analyse 

 mechanical devices into components of mass, resistance and compliance. 

 Every part of a mechanical device possesses mass, and will require a force to 

 accelerate it. This force F^ is given by 



d^x 



F,„ = m 



m 



df2 



where m is the mass, x is the displacement and t is time. Viscous resistance 

 produces a force proportional to the velocity of movement : 



"r = R 



dx 

 It 



where R expresses the magnitude of the viscous effects. It is usual to consider 

 resistance in mechanical circuits as purely viscous, not frictional, for two 

 reasons. First, if resistance is required in a mechanical device it is usually 

 more convenient to employ some form of fluid damping which is more con- 

 trollable than solid friction. Secondly, solid friction gives a maximum force 

 while the body is still stationary, this force falling off" as movement takes 

 place; the mathematical expression of this effect is intractable. In any 

 well-constructed device it is possible to reduce solid friction to small propor- 

 tions by lubrication, and the assumption of purely viscous resistance seldom 

 leads to great inaccuracy. 



CompHance is the property of springs ; it is the reciprocal of the more 

 familiar 'stiffness'. The relationship between force and displacement thus 

 becomes 



where C is the compliance of the spring. The units in which the mechanical 

 components are measured are therefore dynes per cm/sec^ (or grammes) for 

 mass, dynes per cm/sec for resistance and cm per dyne for compliance. 



Mechanical components, like electrical ones, are never 'pure'; a spring 

 possesses some mass, and even the oil in a damping dashpot is slightly 

 elastic. However, as in electrical circuits, one of the components is generally 

 predominant, although neglecting the secondary property of a component 

 may occasionally lead to trouble (c/. page 165). 



Inspection of the three equations given above shows that they are similar 

 to the equations 



given in Chapters 2, 3 and 4 for the voltages across inductance, resistance 

 and capacitance respectively. It is upon this similarity that the use of electro- 

 mechanical analogies is based. The differential equations of a mechanical 

 system are identical to those of an electrical system if for force we write 



473 



