> So things like cams and eccentrics then?

Yep, or just plain linkages of rods and stuff, some of them can get quite 
complex.  On my old Peugeot 206 it had some pretty funky wiper blade 
mechanism to that it would cover much more of the window than a simple arc.

> How is all this related to standing waves?

A standing wave is just a wave that stays in position, ie it's frequency and 
spatial phase remain constant.  If you see a resonant mode by itself, it 
will look like a standing wave and you can easily identify the stationary 
points that remain at rest.

> Presumably a 2D surface like a drum head would have quite a lot of 
> possible resonant modes?

Yep, see these photos that show the stationary points, try to imagine how 
the non-stationary parts would bend up and down.

http://www.meta-synthesis.com/webbook/34_qn/2d_waves.jpg

> Ah yes - just curving the paper makes it behave quite differently. (See 
> corrigated sheet metal.) But why, I wonder?

To curve a flat sheet of paper all you need to do physically is to stretch 
the top half of the thickness by a tiny amount and compress the bottom half 
by an equally tiny amount.  Once you start curving it in other directions as 
well the amount of stretching and squashing you need to perform becomes 
orders of magnitudes higher.  You can see this just by looking at the 
geometry of a curved piece of paper and thinking about how it must deform in 
order to curve it in the other direction.

> Similarly, a hollow tube responds differently to a solid rod.

For a hollow tube and a rod of the same weight, the tube will always be 
stronger and stiffer because it will have a higher 2nd moment of area. 
Actually the I-beam is pretty much the best useful shape you can have, which 
is why they are so common (tubes are not so easy to join together and funny 
angles).

> And again, a tear tends to propogate along a sheet, but if you put a hole 
> in the sheet, it actually stops the tear. WTF?

It's to do with the radius at the tip of the tear (very small) compared to 
the radius of the hole (much bigger).  It's why the windows in aeroplanes 
are round and not square (they had some square ones to start with but they 
got cracks at the corners once the pressure difference went up).

> Presumably there's some molecular-level *reason* for all of this?

Yeh, something to do with dislocations in the crystal lattice from what I 
remember.

> ...because the Laplace transform turns differential equations into 
> algebraic equations?

Yup.

> Did you see Scrappy Races, where the same guy tried to "tune" a 6 L diesel 
> engine, and the govener fell off? (I don't know what a govener is, but it 
> sounds important...)

No I didn't see that one, the governer stops the engine going too fast if 
there is no load.  Diesel engines are quite capable of self-destruction if 
you try to run them flat out with no load.

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