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Title: Lissajous' FiguresPost by: Fu-Kwun Hwang on June 13, 2010, 01:58:21 pm
Lissajous' Figures
When we superpose two simple harmonic movements with perpendicular directions, we obtain a planar movement that is described by the equations x = A1 * cos(w1*t) y = A2 * cos(w2*t + d) where the A's denote the amplitudes of the respective movements (horizontal the first one, vertical the second), the w's denote the respective frequencies and d denotes the phase delay between both movements. If we supply these two signals to the horizontal and vertical inputs of an oscilloscope, its beam will describe a movement that is the result of the superposition of both individual movements and that can adopt several nice figures, depending on the value of the ratio w1/w2 and on d. These curves are called Lissajous' figures and are specially nice for certain values of the parameters. Author : Francisco Esquembre Date : February 2002 Title: Re: Lissajous' FiguresPost by: Fu-Kwun Hwang on June 13, 2010, 02:01:32 pm
Lissajous' Figures
When we superpose two simple harmonic movements with perpendicular directions, we obtain a planar movement that is described by the equations x = A1 * cos(w1*t) y = A2 * cos(w2*t + d) where the A's denote the amplitudes of the respective movements (horizontal the first one, vertical the second), the w's denote the respective frequencies and d denotes the phase delay between both movements. If we supply these two signals to the horizontal and vertical inputs of an oscilloscope, its beam will describe a movement that is the result of the superposition of both individual movements and that can adopt several nice figures, depending on the value of the ratio w1/w2 and on d. These curves are called Lissajous' figures and are specially nice for certain values of the parameters. Author : Francisco Esquembre Date : February 2002 Click image [eye][ejsapplet][/eye] to view another applet |