Period Squared vs. Period (1 Viewer)

nahi11 · Oct 15, 2011

Hi,

What is the reason for squaring the period rather than just the period when displaying it on a graph. I need to do this for the pendulum experiment but don't understand why.

Thanks.

nahi11 · Oct 15, 2011

Thanks.

Is there any other reason?

nightweaver066 · Oct 15, 2011

Well by forming this straight line relationship, you can equate the gradient you measure with the coefficient of 'l' in the formula to work out the acceleration due to gravity.

Fizzy_Cyst · Oct 16, 2011

nahi11 said:
Hi,

What is the reason for squaring the period rather than just the period when displaying it on a graph. I need to do this for the pendulum experiment but don't understand why.

Thanks.

The pendulum equation used in this experiment is:

$T=2\pi\sqrt{\frac{l}{g}}$

by squaring both sides you get:

$T^{2}=\frac{4\pi^{2}l}{g}$

Now by plotting Period squared vs length you get a linear relationship

The gradient of the line would be equal to $\frac{T^{2}}{l}$

So, you can use the gradient to calculate 'g'

By rearranging:

$g=\frac{4\pi^{2}l}{T^{2}}$

therefore

$g=4\pi ^{2}\times \frac{1}{gradient}$

$g=\frac{4\pi ^{2}}{gradient}$

So, plug in your value for the gradient of the period^2 vs length graphj and you can determine acceleration due to gravity

Period Squared vs. Period (1 Viewer)

nahi11

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nahi11

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nightweaver066

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Fizzy_Cyst

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