**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