Example 10.  The initial displacement for a fundamental solution is  .  
Plot the functions for  n = 1,2,3.  
The first fundamental solution vibrates up and down throughout the entire disk of radius 1.
Solution 10.

The first fundamental solution has a circle of radius   as a node where there is no vibration and it moves up and down inside this circle.

The second fundamental solution has a circle of radius   as a node where there is no vibration and it moves up and down in opposite directions on the inside and outside of this circle.

The third fundamental solution has a two circular nodes of radius    and    where there is no vibration and it moves up and down in opposite directions between circles.

(c) John H. Mathews 2004