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When the chalk hits the floor the chances of it hitting at exaxtly
horizontal are vanishingly small. The chalk will first hit at one end
or the other. Thus the chalk is driven with a pulse at the end which
means that the ends oscilate up and down. The least energetic mode
and easiest mode to excite in which the ends are free to oscilate will
be a cosine mode with the lowest number of nodes. In this case there
are two nodes. (see figure) The chalk does not oscillate at the nodes
but does inbetween. There are THREE different regions and adjacent
regions move in opposite directions to one another in time so we
expect a shear to occour near the nodes which will break the chalk
into 3 pieces.
* * * *
^ * * ^
| * * |
| * * |
| * * |
|-------|-------|-------|--------|--
0 * L/2 * L
* | *
* | *
* V *
* *
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