Lissajous Curves: You can make a pendulum swing with different periods in the x- and

Chapter 4, Problem 15

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Lissajous Curves: You can make a pendulum swing with different periods in the x- and y-directions. The parametric equations of the path followed by the pendulum can have the form x = cos nt y = sin t where n is a constant. The resulting paths are called Lissajous curves, or sometimes Bowditch curves. In this problem you will investigate some of these curves. a. Figure 4-7o shows the Lissajous curve with the parametric equations x = cos 3t y = sin t Use your grapher to confirm that these equations generate this graph. b. Plot the Lissajous curve with the equationsx = cos 4t y = sin tSketch the resulting curve. In what way dothe curves differ for n = 3 (an odd number)and for n = 4 (an even number)? c. Sketch what you think these curves wouldlook like. Then plot the graphs on yourgrapher. Do they confirm or refute yoursketches?i. x = cos 5t y = sin tii. x = cos 6t y = sin td. What two familiar curves are special cases ofLissajous curves when n = 1 and n = 2?Bowditch on the Internet or other source.When and where did they live? Give thesources you used