Lissajous patterns

Figure 7. Lissajous patterns representing a polarization modulated electric field over time, viewed in the plane of incidence, resulting from the two orthogonal s and p fields, which are out of phase by the following degrees 0, 21, 42, 64, 85, 106, 127, 148, 169 (top row) 191, 212, 233, 254, 275, 296, 318, 339, 360 (bottom row). In these Lissajous patterns the plane polarizations are represented at 45° to the axes. In this example, there is a simple constant rate polarization with no rotation modulation. This is an SO(3) Q (a>, 8) in C representation over 2n, not an SU(2) <2 (t /, %) in C over it.

Figure 2.36 shows a schematic of an experimental set-up proposed by Spinner and Teft (1961). The specimen is suspended from the driver and pick-up, both of which are usually piezoelectric transducers. The oscilloscope and voltmeter (or ammeter) are used to accurately determine the exact resonant frequency and its maximum amplitude (using Lissajous patterns, see Schreiber et al. (1973)). Alternatively, electronic audio equipment is now available to induce a wide range of vibration frequencies and the ensuing acoustic spectrum can be obtained by a Fourier transform. 

Lissajous pattern The looping patterns generated by a CRT spot when the horizontal (X) and vertical (Y) deflection signals are sinusoids. The lissajous pattern is useful for evaluating the delay or phase of two sinusoids of the same frequency. 

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 ]. 

Most of the proteins and enzymes that we want to study have a photocycle time longer than 1 ms. Therefore, to ensure a fresh sample spot for each laser shot, we designed a Lissajous sample scanner. In short, the sample is moved perpendicular to the beam on three eccentrics that lead to a scan pattern filling a 20x20 mm surface. The velocity in the comers and at the sides is too low to refresh the sample after each laser shot, therefore these shots are discarded (-16-18%). The laser comes back at the same sample position after about a minute. 

Fig. 2. Scan pattern of the Lissajous sample scanner, filling a 20x20 mm CaF2 surface in about 1 minute.

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... 

Figure 7.21 (a) Effective lissajous condition for linear conditioning and (b) zonal conditioning pattern. 

In this experiment, plug in the transformer and use its 12 V secondary instead of the bahery. With the X versus Y type of scope display, a continuous oval pattern is observed, which is called a "Lissajous figure," named after an early scientist. The vertical VOLTS/DIV knobs, and also their smaller VARIABLE knobs, can be adjusted to other settings such as >5V / div for X and <20 mV / div for Y, in order to make the scope pattern become nearly a perfect circle. 

Figure 24 PS548/D0P 6.0wt.% at27°C under osciiiatory shear fiow (a) phase diagram in the parameter space of yoand to (b)the Lissajous figures at points (A)-(C) in the phase diagram shown in (a). The circies andtriangies in part (a) indicate the point (to,yo) where the butterfiy patterns were observed, whereas the crosses indicate the point where no SALS patterns were observed.

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