Lissajous figure

Consider for definiteness the antisymmetric case. We choose the origin of the coordinate system in one of the wells, and the center of symmetry has the coordinates Qt,Q-) (fig- 31). Inside the well the classical trajectories are Lissajous figures bordering on the rectangle formed by the lines Q = Q , and Q = —Q , where Q are the turning-point coordinates. 

The alternate method uses the proximity probes and an oscilloscope. A Lissajous figure is established on the oscilloscope. The orbit pattern and the keyphase mark are used to generate a vector. Weights are added or removed and the changes in the orbit are noted. Triangulation is used to anticipate the next move. For more complete information or technique, the reader is referred to a book on the subject by Jackson [ 1 ]. 

Lissajous figure. 378 Loop testing, 417 Lube and seal system specification information, 449... 

The Martindale abrader is usually seen as a four station machine which uses cloth as the abradant, but coarser and faster acting materials can be substituted. The principal feature of this machine is that the test pieces are rubbed successively in different directions as the motion takes the form of a Lissajous figure. It is mostly used with coated fabrics62. 

As shown in Fig. 11.3, the values of the important variables can be taken directly from the Lissajous figure. 

Lissajous figure. Set the selector switch on the scope to horizontal input. Now both the horizontal and the vertical inputs come from the oscillator. Generally an ellipsoidal pattern will be seen on the scope. The width (minor axis) of the ellipse can be reduced by balancing the reactance. The null point occurs when the major axis of the ellipse is as nearly horizontal as possible. 

One application of an analog oscilloscope is in examining the relative phase relationship of two sinusoidal wave forms, one of which (of frequency is supplied to the vertical input (/) of the oscilloscope, the other (of frequency /j/) to the horizontal input (x). When the display mode is chosen to be. v vs. /, the. v voltage replaces the internal sawtooth sweep voltage and the oscilloscope becomes a sensitive device for comparing the frequencies of the sine waves. When the ratio of the frequencies is a rational fraction, a symmetrical closed pattern called a Lissajous figure will appear on the screen. The frequency ratio can be obtained from the form of the pattern by using the formula... 

Lissajous figures (a) several simple figures, witii tiie ratios /j indicated b) the 1 1 figure for various values of die phase angle between signals of equal amphtude. 

Consider the case where a circular annulus of fluid is undergoing circular motion at radius r with angular speed w. The two-dimensional VEXSY spectrum has the character of a Lissajous figure ... 

Unusual stress waveforms are observed during oscillatory deformation on such materials when the strain amplitude is much greater than the yield strain. Watanabe and Kotaka (1984) plotted large-amplitude oscillatory shear data in the form of Lissajous figures— that is, plots of periodic stress versus periodic strain. In the nonlinear regime, above the yield strain, unusual rhombic Lissajous figures were obtained at low frequencies, and bent ellipses were obtained at higher frequencies. Qualitatively, the waveforms are similar to those depicted in Fig. 13-23. 

The predictions of the theory of Doi et al. (1993) are in good qualitative agreement with experiments on diblock copolymers with ordered spherical domains. In particular, the theory predicts that peculiar Lissajous figures (Fig. 13-23) observed by Watanabe and Kotaka... 

Plotting Lissajous figures) Using a computer, plot the curve whose parametric equations are x(t) = sinr, y t) =sin(yf, for the following rational and irrational values of the parameter cu ... 

The resulting curves are called Lissajous figures. In the old days they were displayed on oscilloscopes by using two ac signals of different frequencies as inputs. 

Explaining Lissajous figures) Lissajous figures are one way to visualize the knots and quasiperiodicity discussed in the text. To see this, consider a pair of uncoupled harmonic oscillators described by the four-dimensional system. r-)-x = 0, y + co y Q. 

There is an intrinsic experimental problem when using magnetic field modulation in ESR spectroscopy that is associated with spurious resonance-like modulations transferred to the microwave carrier and arising from modulations of the resonator microwave characteristics. This phenomenon, perhaps apocryphally, was called potato by F. Bloch because of the resemblance when the effect is displayed as a lissajous figure. 

Lissajous analysis is another method of presenting MTDSC data that allow the operator to monitor whether the sample is in steady state or otherwise. In the case of MTDSC, the Lissajous figure is obtained by plotting the derivative of the mod-... 

FIGURE 4.5 Schematic of a typical Lissajous figure (after TA Instruments). (From Jiang, Z., Imrie, C.T., and Hutchinson, J.M., Thermochim. Acta, 387, 75, 2002. With permission.)... 

Fig. 6.—Curve representing the motion of a system with two degrees of freedom, in which the two frequencies I l and I a are incommensurable (Lissajous figure).

LEFT Voltage (above) and current waveforms RIGHT Lissajous figure... 

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