21.3 Sensor Choices

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Box 21.1 shows some representative sensors for damping measurements. The list is far from exhaustive;

for a detailed description of each (plus discussion of other types), the reader is referred to Fraden (1996).

Of the transducer types indicated, position sensors are generally the most versatile; but the present

chapter also provides examples of the use of (i) velocity, (ii) microphone, and (iii) photogate

measurements.

In addition to the need for linearity (discussed in Section 21.1 above), the ideal sensor will be

noninvasive. In reality, it is not possible to perform a measurement that does not at some level perturb

the system under study. The least perturbative types of direct measurement are optical and electrical —

capacitive, followed by inductive.

Some of the advantages and disadvantages of the devices indicated in Box 21.1 are provided below.

21.3.1 Direct Measurement

21.3.1.1 Position Sensors

The inductive linear variable differential transformer (LVDT) is a sensor that is commonly used in

engineering applications. Thus, it has been a natural choice for many position-sensing purposes; but it is

both more invasive and noisier than capacitive sensors. Wielandt (2001) notes the following concerning

the advantage of capacitive over inductive sensors: “Their sensitivity is … typically a hundred times

better than that of the inductive type.”

Optical encoders are also readily available and have been used extensively. Because of their digital

nature, based in a finite number of elements, their low-level resolution is poor compared to capacitive

devices.

Box 21.1

SOME SENSOR TYPES

Representative Sensors for Damping Measurements

Position Velocity Pressure Time Interval Acceleration Force/Strain

Capacitive Faraday law (electromagnetic) Microphone Photogate Accelerometer Strain gauge

LVDT Pressure gauge

Optical Capacitive

Encoder Optoelectronic

Shadow Piezoresistive

Potentiometric

Experimental Techniques in Damping 21-7

© 2005 by Taylor & Francis Group, LLC

Optical sensing by shadow means is easy to employ — for example, using a solar cell of the type

discussed later. The method is afflicted, however, by (i) an offset voltage, and (ii) the degrading influence

of background light.

Potentiometers are very easy to use, but compared to other position sensors they are extremely invasive

because of Coulomb friction in the slider and also the bearings that support it.

21.3.1.2 Velocity Sensor

The most important velocity sensor is that which functions on the basis of Faraday’s law. Using a magnet

and a coil, an electromagnetic force is generated in the wire of the coil when it experiences a changing

magnetic flux. Prevalent in seismometers before the advent of broadband (feedback) instruments, its

primary shortcoming is poor sensitivity at low frequencies.

21.3.1.3 Time Interval

Photogates have become the primary means for kinematic studies in introductory physics laboratories.

Combined with compact, user-friendly timers, it is possible to measure both period and velocity. As

illustrated later, they can be easily used to measure damping in slowly oscillating systems, but only in a

limited amplitude range.

21.3.2 Indirect Measurement

In the cases of (i) pressure, (ii) acceleration, and (iii) force/stress sensing, the measurement is an indirect

one. Consider, for example, the Ruchhardt experiment to measure the ratio of heat capacities of a gas

(discussed in Chapter 20). The oscillation of the piston could be measured in several different ways. For

instance, direct position sensing could be accomplished by attaching a small electrode to the piston and

allowing it to move between stationary capacitor plates. Alternatively, a “flag” on the piston could be used

to interrupt the light beam of a photogate. Depending on constraints, however, the easiest method might

be an indirect measurement in which a pressure sensor monitors the gas through a catheter

communicating with the cylinder of the apparatus.

Accelerometers can sometimes be connected directly to an oscillator, but only if the mass of the

instrument is very small compared to the system being studied. As with the measurement of velocity,

their sensitivity at low frequency is very poor (the second derivative of position yielding a response that is

proportional to frequency-squared).

Strain gauges are easy to employ but also lack sensitivity (compared to position measurement), since

they communicate with a very small portion of the oscillating sample (if noninvasive).

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