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The other day, I told a friend of mine that the period of a simple pendulum is independent of its amplitude (as long as the angles are small). She didn't believe me, so I demonstrated it to her. She admitted that it was true, but still doesn't understand why they are independent. My problem is, she knows no math beyond fractions, and is pretty uncertain about those. So, please give me a clear, non-mathematical, physical explanation for why the period of the simple pendulum is independent of its amplitude (for small angles) that she will understand. Thanks!

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Edited Tue, 01 Dec '15
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The equation for time peroid of simple pendulum is
T=2pi*sqrt(l/g)
from equation we can say that
Time period depends only on "l = lenght of the pendulum" and "g=acceleration due to gravity"
it does not depend on Amplitude
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