The simple pendulum

Reply Sat 29 Sep, 2012 03:47 pm

Please read the link above first.

I do not understand how we substitute mg/L for k. According to Hooke's law x stands for displacement. But thing is I can't see ANY displacement in the simple pendulum. How in the earth could the ARC x become the displacement x.

Hooke's law: x = displacement
The simple pendulum: x = arc

I don't get it. Especially how we say the arc x suddenly started to be used as the displacement x. How it fits?
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Reply Tue 2 Oct, 2012 02:36 pm
Cici you might have to access a more technically oriented forum
Reply Tue 2 Oct, 2012 04:43 pm
Do you know such a forum?
Reply Tue 2 Oct, 2012 05:08 pm
No Cici but go to Google and try inputs like "mathematics physics forums"
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Reply Tue 2 Oct, 2012 06:15 pm
Along the middle of this page is a very good explanation on it.

Don't get confused by the difference of x and s (arc length). The picture you posted uses x as the arc length, while the explanation in the link uses s as the arc length.
Reply Tue 2 Oct, 2012 06:25 pm
Don't get hung up on the small angle approximation.
To understand small angle approximation better, just think that when taking small angle approximation, the amplitude of the pendulum has no effect on the period, and without the small-angle approximation the differential equations used is not the simple harmonic motion (SHM) equation and the period is not independent of the amplitude.
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