1. Lissajous figures describe the patterns that result from combining two harmonic oscillations with different frequencies or phases. 2. The shapes of the Lissajous figures depend on the frequency ratio and phase difference between the two oscillations. Common shapes include straight lines, ellipses, circles, and figure-8 patterns. 3. Lissajous figures can be used to determine the frequency ratio between two oscillations by counting the number of times the pattern crosses the x- and y- axes in a given time period. This provides a way to measure unknown frequencies.