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ArrowLissajous Figures on an Oscilloscope

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Lissajous figures are patterns generated by the junction of a pair of sinusoidal waves with axes that are perpendicular to one another. The figures, sometimes called Bowditch curves, were first described in the early 1800s by American mathematician Nathaniel Bowditch, who experimented with a pendulum undulating around perpendicular axes at the same time. Later that century, French mathematician Jules-Antoine Lissajous began his own study of the figures, which he produced in multiple ways. One of his methods involved creating vibrations in a mirror with sounds of different frequencies, then reflecting light from that mirror to produce various patterns. More commonly today, Lissajous figures are generated with an oscilloscope, a type of cathode ray tube that provides a picture of electrical signals in the form of a graph.

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This tutorial is a three-dimensional simulation of a cathode ray oscilloscope producing Lissajous figures as it compares sinusoidal voltages. To change the viewing angle, click and drag the figure. To restore the figure to the original view, click the Front View button.

Included in the simplified illustration are a cathode ray gun, which produces the Lissajous figures on the oscilloscope screen by means of an electron beam that causes a glow when it hits the scope’s surface, which is coated in phosphor. Also pictured are horizontal and vertical deflection plates, which work in tandem to deflect the electron beam (made up of negatively charged electrons) across the screen. They do this by means of electrostatic deflection. This happens when a potential difference is created across one pair of plates, bringing about an electric field through which the electron beam passes. When one of a pair of plates is positive with respect to its opposing plate, the beam is deflected in that direction. In this manner the beam can be deflected up, down, right or left in a way that covers the entire grid of the oscilloscope screen.

In this tutorial, deflection plates are colored red when positive, black when negative.

Various fixed geometric shapes and patterns can be produced on the oscilloscope screen by selecting the desired option from the Choose a Preset pull-down menu. A much wider range of Lissajous figures can be created by manually adjusting the amplitude, frequency, and/or phase of one or both of the voltages via the designated sliders. The Reset button can be clicked to restart the production of any particular figure by the cathode ray gun, and the Speed slider can be moved to the right or left to increase or decrease the amount of time required to produce the patterns.

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