The simple pendulum

Forums: Pendulum, Physics
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http://i.imgur.com/lv9Kv.png

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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Type: Question • Score: 2 • Views: 962 • Replies: 5

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@cicibebe,

Cici you might have to access a more technically oriented forum

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@dalehileman,

Do you know such a forum?

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@cicibebe,

No Cici but go to Google and try inputs like "mathematics physics forums"

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@cicibebe,

Along the middle of this page is a very good explanation on it.
http://dev.physicslab.org/Document.aspx?doctype=3&filename=OscillatoryMotion_PendulumSHM.xml

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.

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@Enzo,

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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The simple pendulum

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