Example 16
Surface, Contour, and Density Plots

Copyright © 1993 by Bill Titus, Carleton College, 
Department of Physics and Astronomy, Northfield, MN  55057-4025
September 6, 1993

Topics and Skills

Problem

Solution

Step 1 - For simplicity, assume that  a = 1,   c = 1,  and  α = 0.  Use the MMA command  Plot3D[]  to plot the surface of the sheet at time  t = 0  for the normal mode corresponding to  n = 1  and  m = 2.  Don't include any options in the plot command.

Comment 1

Step 2 - Examine the options for  Plot3D[]  and use some of them to label your axes and change to surface color to red.

Step 3 - Now choose options to remove the axes and the bounding box so that the sheet just sits there in free space.  Keep the surface color red, but increase the number of  PlotPoints  to  30  so that the surface is smoother.

Comment 3

Step 4 -  Practice changing the viewpoint at which you observe the free surface.  You might want to use the 3D ViewPoint Selector to help you out.

Step 5 - Create a table of ten plots for  t   going from  0  to  2Pi/w.  Then animate your surface's motion as a function of time.  To speed up the drawing, set  PlotPoints  to  15.

Step 6 - Now make a contour plot of the surface at time  t = 0  for the normal mode corresponding to  n = 1  and  m = 1.  As before, assume that  a = 1,  c = 1,  and  α = 0.  Locate the appropriate MMA command to accomplish this task, and apply it without any of its options.

Step 7 -  Play with some of the options to  ContourPlot[]  to enchance the appearance of the normal mode plot.

Comment 7

Step 8 - Repeat Step 7, but now use the MMA command  DensityPlot[]  and some of its options.

Comment 8

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