Experiment 6:Lissajous Figures Introduction Suppose a particle is traveling in harmonic motion in two dimensions,such that its equation of motion is: x=A,cos(ot+,)y=A,cos(ot+,) Since the motion of the particle in the x and y directions have the same frequency,they also have the same period,T.So,no matter where the particle is at time t,it will be back at the same point at time t+T.The path of the particle therefore,forms a closed loop. You can produce a similar sort of motion on an oscilloscope by using one waveform from the Fourier Synthesizer to control the horizontal motion of the electron beam and other waveform to control the vertical motion.Since All the waveforms of the Synthesizer are harmonics of the fundamental,the trace on the oscilloscope will always be a closed loop.These closed loops ate known as Lissajous figures,after Jules Antoine Lissajous. Procedure 1.Connect the ground jack of an oscilloscope to one of the ground jacks on the Fourier Synthesizer 2.Connect the vertical input of the scope to one of the 10k OUTPUT jack of the first fundamental. 3.Connect the horizontal input of the scope to the 10kQ OUTPUT jack of the second fundamental. 4.Adjust the amplitude and phase of the second fundamental.Then do the same with the first fundamental.Discuss how amplitude and phase variations affect the shape of the Lissajous figure.What amplitude and phase relationships are necessary to create a circular pattern? 5.Try switching one or both of the fundamentals to a square or triangular wave,Again,vary the phase and amplitude and notice the changes in the curve.Try to relate the shape of the curve with the shape of the individual waveforms. 6.Try using higher harmonics for one or both of the oscilloscope inputs.Can you make any generalizations about the shape of the curve and the harmonic used? 7.To make more complicated curves,try using the 10kQ output of the summing amplifier as one of the inputs.8 Experiment 6: Lissajous Figures Introduction Suppose a particle is traveling in harmonic motion in two dimensions, such that its equation of motion is: cos( ); x x x = A t + cos( ) y y y = A t + Since the motion of the particle in the x and y directions have the same frequency, ω they also have the same period, T. So, no matter where the particle is at time t, it will be back at the same point at time t+T. The path of the particle therefore, forms a closed loop. You can produce a similar sort of motion on an oscilloscope by using one waveform from the Fourier Synthesizer to control the horizontal motion of the electron beam and other waveform to control the vertical motion. Since All the waveforms of the Synthesizer are harmonics of the fundamental, the trace on the oscilloscope will always be a closed loop. These closed loops ate known as Lissajous figures, after Jules Antoine Lissajous. Procedure 1. Connect the ground jack of an oscilloscope to one of the ground jacks on the Fourier Synthesizer. 2. Connect the vertical input of the scope to one of the 10kΩ OUTPUT jack of the first fundamental. 3. Connect the horizontal input of the scope to the 10kQ OUTPUT jack of the second fundamental. 4. Adjust the amplitude and phase of the second fundamental. Then do the same with the first fundamental. Discuss how amplitude and phase variations affect the shape of the Lissajous figure. What amplitude and phase relationships are necessary to create a circular pattern? 5. Try switching one or both of the fundamentals to a square or triangular wave, Again, vary the phase and amplitude and notice the changes in the curve. Try to relate the shape of the curve with the shape of the individual waveforms. 6. Try using higher harmonics for one or both of the oscilloscope inputs. Can you make any generalizations about the shape of the curve and the harmonic used? 7. To make more complicated curves, try using the 10kQ output of the summing amplifier as one of the inputs