Oscilloscope Patterns of Damped Vibrations of Quartz Plates and Q Measurements with Damped Vibrations

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Abstract
The first part of the paper describes a method of obtaining a picture of the damped vibrations of a quartz-plate resonator which occur when the excitation is removed by short-circuiting the electrodes between which the quartz plate lies. The build-up of vibrations after the short-circuit is removed is also shown. The quartz plate is short-circuited by means of a rotating commutator, and the resulting damped short-circuit current is caused to give a stationary damped-wave pattern on the cathode-ray-oscilloscope screen. Photographs of the patterns are easily obtained. Some interesting effects, such as variation of electrode air gap and pressure, are observed, and a few examples are shown. Since the damping or the Q of a circuit may be readily determined from the formula S = 1/n log A1/(An+1) applied to n decaying amplitudes from A1to An+1the logarithmic decrement is readily found. The Q is also readily found since it is related to the reciprocal of δ. Amplitudes A1and An+1may be measured on the screen or photograph of the pattern for determination of δ or Q, but a more satisfactory method of measurement of these quantities was developed, incorporating a form of the commonly used momentary contactor, such as is sometimes used in the determination of wave form of an alternator. The speed of the contactor provides a ready determination of the number of vibrations from A1to An+1. A working formula [equation (3)] is developed for rapid measurements of Q of the quartz plate.

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