Question:
I have been trying to prove gravity using only the period of a pendulum. I have
tried any possible way, and I still cannot do it. How do you solve for gravity using only the
period of a pendulum?

Replies:
Dear Lyndsey,

I am not sure what you mean by "prove" gravity. "Prove" its existence as a force, or prove
that the measured value is 9.8 m/s2?

If it is indeed the latter, I can think of two ways. E-mail me again and explain what you have
done so far. If I can see how you have approached the problem; I can probably point you in
the right direction.

If you are talking about messing with equations; you probably have something like this
already: p stands for pi. My symbol does not seem to transfer to e-mail

T is approximately = 2p X the square root of the quantity ( I/ mgh) where I is = mL2.

You can substitute the mL2 for the I, giving you ( mL2/ mgL) under the radical sign. This in
turn can be reduced to

T is approx.= 2p X the square root of (L/g).

If you square everything to get rid of the radical sign, it looks big and hairy like this:

T2 is approximately = 4p2 L/g

This approximately = to business can be equal as long as the pendulum does not have a big
amplitude.

Rearrange and solve for g

g= 4p2 L/T2

E-mail me back if this does not make sense. I will try sending an attachment next time.

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