> You can have a few more points if you explain the "in the limit of small 
> elongations" part...

You can write an exact differential equation for the motion of a pendulum, 
but it will have a sin or cos in it because the string/rod is at an angle to 
gravity.  Usually you replace sin(x) with just x to make it easy to solve 
and get a simple solution.  x (in radians!) is actually a pretty good 
approximation to sin(x) for angles up to 10 or 20 degrees - try it. 
Obviously the bigger swings your pendulum makes, the more inaccurate the 
"simple" equation will be.

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