Δ = π / 4, a = 5, b = 4 (5:4)Generation Prior to modern electronic equipment, Lissajous curves could be generated mechanically by means of a.Practical application Lissajous curves can also be generated using an (as illustrated). An can be used to demonstrate the images on an oscilloscope.
Aug 11, 2016 The device connects a current-limited voltage to the component or circuit of interest. Voltage and current are plotted in the display of an oscilloscope operating in XY mode, and the Lissajous patterns convey information to the user regarding the status of the device or circuit.
Two phase-shifted sinusoid inputs are applied to the oscilloscope in X-Y mode and the phase relationship between the signals is presented as a Lissajous figure.In the professional audio world, this method is used for realtime analysis of the phase relationship between the left and right channels of a stereo audio signal. On larger, more sophisticated audio mixing consoles an oscilloscope may be built-in for this purpose.On an oscilloscope, we suppose x is CH1 and y is CH2, A is the amplitude of CH1 and B is the amplitude of CH2, a is the frequency of CH1 and b is the frequency of CH2, so a / b is the ratio of frequencies of the two channels, and δ is the phase shift of CH1.A purely mechanical application of a Lissajous curve with a = 1, b = 2 is in the driving mechanism of the type of oscillating beam lamps popular with railroads in the mid-1900s. The beam in some versions traces out a lopsided figure-8 pattern on its side.Application for the case of a = b. Top: Output signal as a function of time.Middle: Input signal as a function of time.Bottom: Resulting Lissajous curve when output is plotted as a function of the input.In this particular example, because the output is 90 degrees out of phase from the input, the Lissajous curve is a circle, and is rotating counterclockwise.When the input to an is sinusoidal, the output is sinusoidal with the same frequency, but it may have a different amplitude and some. Using an that can plot one signal against another (as opposed to one signal against time) to plot the output of an LTI system against the input to the LTI system produces an ellipse that is a Lissajous figure for the special case of a = b. The of the resulting ellipse is a function of the phase shift between the input and output, with an aspect ratio of 1 (perfect circle) corresponding to a phase shift of ±90° and an aspect ratio of ∞ (a line) corresponding to a phase shift of 0° or 180°.
The figure below summarizes how the Lissajous figure changes over different phase shifts. The phase shifts are all negative so that can be used with a LTI system (note that −270° is equivalent to +90°). The arrows show the direction of rotation of the Lissajous figure. Science fiction style Lissajous animationLissajous figures were sometimes displayed on oscilloscopes meant to simulate high-tech equipment in science-fiction TV shows and movies in the 1960s and 1970s.The by for 's 1958 film is based on Lissajous figures.In a sequence towards the end of an episode of Columbo entitled 'Make me a Perfect Murder', the detective sits watching Lissajous curves displayed to music on monitors in a TV outside broadcast van.Company logos Lissajous figures are sometimes used in as. Examples include:.
The ( a = 1, b = 3, δ = π / 2). The at ( a = 4, b = 3, δ = π / 2). The, Japan ( a = 5, b = 6, δ = π / 2). Disney's streaming video application uses a stylized version of the curveIn modern art.
Generating various Lissajous Figures on an oscilloscope make a very interesting experiment. Apart from that, these curves are of particular value in electronics, serving to identify the characteristics of any unknown electric signal when compared to a known one.Traditionally, generating Lissajous Figures where the frequencies of the input signals are unequal require the use of two synchronized signal generators or a multi-channel function generator.
But, nowadays most PCs and Laptops come equipped with a stereo audio output jack. This output can be used as a synchronized 2-channel signal generator and can be used to generate various Lissajous Figures on an oscilloscope.You will need:1. A PC/Laptop with a stereo audio output2. A 3.5mm stereo aux cable3. Audacity v.2.0 or above.
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