I     INTRODUCTION

This article describes precision optical techniques for measurement of pendulum period, using either new test equipment, or older, used test equipment. We develop a digital delay line of counter circuitry, to be used for the precision delay of the final, delayed-sweep oscilloscope. The function is identical to that in a digital delayed-sweep oscilloscope, even though we require only an analog oscilloscope, without the delayed-sweep function. Many types of used test equipment, or new test equipment may therefore be used with these analog and digital circuits, including many analog oscilloscopes, digital oscilloscopes, PC-based oscilloscopes, ethernet USB oscilloscopes, data acquisition boards, and oscilloscope boards.

Precision methods for measuring pendulum periods are necessary for development, testing and verification of both conventional, and new pendulum types [1-3]. These include elliptical pendulums and cycloidal pendulums, as shown in Fig. 1, which do not exhibit circular error. They are also useful for measuring the variation of period with amplitude [4] of circular pendulums, and measuring barometric and temperature effects on pendulum period. As the perturbation due to the clock’s escapement is usually considerably larger than these effects to be measured, it is only possible to obtain clean and reliable measurements if the pendulum is observed in free oscillation, without any escapement. Optical techniques offer by far the best accuracy, as they require no connection to the pendulum. Such optical methods have been used since the 1930’s in electric pendulum regulators [5], to synchronize the electromagnetic impulse to the pendulum.