Chapter 13.6, Problem 1P

1. Continue Figure 6.1 to show the fundamental modes of vibration of a circular membrane for $n=0,1,2,$ and $m=1,2,3.$ As in Figure 6.1,write the formula for the displacement $z$ under each sketch.
2. Use a computer to set up animations of the various modes of vibration of a circular membrane. [This has been discussed in a number of places. See, for example, Am. J. Phys. $67,534-537,(1999).]$