What are the Lissajous figures in physics?
Contents
What are the Lissajous figures in physics?
A Lissajous figure is a curve formed by the superposition of two perpendicular simple harmonic motions.
What is the significance of Lissajous figure?
The Lissajous figure is of high importance in physics in order to study the sinusoidal waves. The Lissajous figures are mainly used in analogue electronics to analyse the intersection of two or more sinusoidal wave constructing loops which is also known as knots in general.
What is lissajous method explain it?
The Lissajous pattern indicates the phase difference by the shape of the X-Y plot. A straight line indicates a 0º or 180º phase difference. The angle of the line depends on the difference in amplitude between the two signals, a line at 45º to the horizontal means the amplitudes are equal.
How can you produce an ellipse in a Lissajous figure?
Using an oscilloscope 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.
Where do Lissajous figures appear?
A Lissajous figure is displayed on the screen when sinusoidal signals are applied to both horizontal & vertical deflection plates of CRO. Hence, apply the sinusoidal signals, which have same amplitude and frequency to both horizontal and vertical deflection plates of CRO.
How do you read Lissajous figures?
Lissajous curves are given by the two parametric equations shown here. Their appearance is sensitive to the ratio a/b. When a/b= 1, the figure is an ellipse. The ratio a/b also determines the number of lobes in the figure — ratios of 3/1 or 1/3 produce figures with three major lobes.
Where do Lissajous figure appear?
How Lissajous figures are produced?
Lissajous figure, also called Bowditch Curve, pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. Lissajous used a narrow stream of sand pouring from the base of a compound pendulum to produce the curves.
What is Lissajous figure in SHM?
If two S.H.M’s act in perpendicular directions, then their resultant motion is in the form of a straight line or a circle or a parabola etc. depending on the frequency ratio of the two S.H.M. and initial phase difference. These figures are called Lissajous figures.
How Lissajous figures are formed?
Which is the correct name for the Lissajous curve?
A Lissajous curve / ˈlɪsəʒuː /, also known as Lissajous figure or Bowditch curve / ˈbaʊdɪtʃ /, is the graph of a system of parametric equations which describe complex harmonic motion.
How are Lissajous figures produced in two dimensions?
Lissajous figures (or Lissajous curves) are produced in two dimensions when the x and y coordinates are given by two sine waves, which may have any amplitude, frequency and phase. This is a support page to the multimedia chapter Interference and Consonance in the volume Waves and Sound, which introduces interactions between sine waves.
In physics, harmonic vibration is a type of periodic motion where the restoring force is proportional to the displacement. If you haven’t seen harmonic vibrations before, please read through this helper page before proceeding, since this concept is crucial in our following discussion of Lissajous Curves.
Why does the Lissajous curve rotate counterclockwise?
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 LTI system is sinusoidal, the output is sinusoidal with the same frequency, but it may have a different amplitude and some phase shift.