> So if you wanted to describe the motion of a complex arrangement of rigid 
> components (e.g., a car gearbox), you'd use kinematics?

Yes, for analysis of how fast each bit spins, but that part is actually very 
simple and well known about gearboxes.  Kinematics would be more useful to 
design the windscreen wiper mechanism for instance, where it is assumed that 
the motor can generate enough torque to maintain a constant speed.  What the 
designer must consider is how the constant angular velocity of the electric 
motor is converted to that movement you see the wiper blades making.

> So... the resonant modes of a effectively 1D system (a string, a 
> gas-filled pipe, etc.) would just be harmonics of the main resonant 
> frequency?

Haha I should have known this had something to do with organ pipes!  Yes 
pretty much.

> Heh. So you know how an ideal gas is different from a real gas then? ;-)

From what I recall, ideal gasses are ones that follow the PV=nRT equation 
and a host of other equations.  Which works pretty well for most "normal" 
gasses at "normal" temperature and pressure.  IIRC it doesn't work for steam 
though, which is why we needed hideous fold-out tables and charts.

> If I take a piece of paper and hold it horisontal, it flops under its own 
> weight. But if I fold it down the middle, now it *can* stand up under its 
> own weight. (But only if you hold it the right way.)

You can do that without folding it too, along the edge that you are holding 
it, just push down in the middle with your thumb above the paper with two 
fingers underneath either side.  By introducing that slight curvature in the 
paper you are making it very difficult to bend downwards without stretching 
or ripping the paper, so of course then the paper does not have enough 
weight to do that by itself.  I don't know what category this would come 
under, dynamics or thin bodies or something ;-)

> At the same time, a straight metal rod is very strong, but once bent it 
> becomes drastically weaker,

Actually it usually becomes stronger after the 1st bend because you have 
work hardened it at that point.

> and it seems that nothing will restore it to its original condition.

Because when you try to bend it back, it just wants to bend at a different 
point rather than where the original bend was, because that point is now 
stronger!  Eventually of course if you repeatedly bend it enough fatigue 
will set in and it will break.

> Wait - there's a way to *solve* differential equations?? o_O

Use Laplace transforms, makes things way easier for non-trivial differential 
equations.

> OMG, the first time I watched this on TV, I killed myself laughing. All 
> those hours to build, and it ****ed itself to pieces in seconds! :-D

Hehe yeh I love that program.  Our robot almost did the same, when I 
disconnected the control interface to the PC while the motor that lifted the 
arm was still running.  Of course it was in software that the motor is 
stopped when it hits the switch at the end of the arm's travel, so with no 
more control input the motor continued to wind up and start bending the 
metal arm before I could pull the power :-)  The mechanics guys weren't 
pleased that they had to rebuilt it.

> By the way... how much of the stuff you learnt do you actually *use* now 
> anyway? ;-)

Around 10% probably, but I would imagine every job would have a slightly 
different 10% so I certainly don't regret doing such a wide range of 
subjects within Engineering.

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