Aim Study the nature of Lissajous
Aim: Study the nature of Lissajous figures that formed by the combination of two perpendicular SHM of different amplitude and frequencies using computer programming
Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows.
Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.
Applications of Lissajous figures
Calibration. Based on the idea that the nonlinearities of devices contain useful information, outputs from twin encoder detectors can be plotted against one another to reveal sensor miscalibration. Potato-shaped plots imply imperfect alignment of the light source, encoder disc, and/or photodetectors.
triangle wave A triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.
Like a square wave, the triangle wave contains only odd harmonics, due to its odd symmetry. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse).
square wave
A square wave is a non-sinusoidal periodic waveform (which can be represented as an infinite summation of sinusoidal waves), in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. The transition between
Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows.
Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.
Applications of Lissajous figures
Calibration. Based on the idea that the nonlinearities of devices contain useful information, outputs from twin encoder detectors can be plotted against one another to reveal sensor miscalibration. Potato-shaped plots imply imperfect alignment of the light source, encoder disc, and/or photodetectors.
triangle wave A triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.
Like a square wave, the triangle wave contains only odd harmonics, due to its odd symmetry. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse).
square wave
A square wave is a non-sinusoidal periodic waveform (which can be represented as an infinite summation of sinusoidal waves), in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. The transition between