MECHANICAL PROPERTIES OF TRANSDUCERS 



A pen is constrained to move linearly by a slide of mass m. A spring of 

 compliance C controls the movement of the slide, and the force to be 

 measured is applied through a tension wire. The slide is lubricated and is 

 subject to a viscous resistance R. The simple approach gives the linear 

 movement of the slide as proportional to ths force applied. 



Spring 



Slide 



Pen 



Tension 

 wire 



Figure 33.1 Force-recording apparatus 



In drawing the electrical equivalent circuit it will be seen that all three 

 components, mass, resistance and compliance, have the same displacement, 

 and that the equivalent circuit thus has inductance, resistance and capacitance 

 in series (Figure 33.2). The applied force is the applied voltage; the velocity 

 of the pen is the current in the circuit. 



m 



R 



c 



V 



Figure 33.2 Equivalent circuit of force-recording apparatus 



Since the pen's displacement, not its velocity, is required, it is necessary 

 to use one of the equations : 



x = Jy d?, ^ = J/ d/ 



A useful artifice to avoid this integration uses the fact that the voltage 

 across the condenser is given by the equation 



475 



