Non-Harmonic Pendulum: Calculating Gravity g

[Rosella Lin]

If the Pendulum doesn't follow Harmonic Motion can we still use the formula

1) T = 2π Root(L/g) ?

2) If not, how can I calculate gravity g?

 

[S.G. Janssens]

1) No, this is only true in the small angle approximation.
2) You could simply start from a small angle, so the amplitude-independent formula for the period holds. If you insist on starting from an arbitrary angle, you need to deal with an elliptic integral, see e.g. here. There is a lot of literature on this topic, but if your purpose is to find the value of $g$, other methods are perhaps better.

 

[Rosella Lin]

Thank You ! :)

 

[S.G. Janssens]

In fact, upon closer inspection, it does not seem too hard to determine $g$ starting from a large angle either. If you have a look at that Wikipedia-link I gave and you go to the section "Arbitrary-amplitude period", you can see that $T$ is the product of $4\sqrt{\tfrac{\ell}{g}}$ and an elliptic integral that depends on $\theta_0$ (the amplitude), but not on $g$. So, if in your experiment you measure $\theta_0$ and $\ell$ and then compute the elliptic integral numerically (or from a table) using your measured value of $\theta_0$, you can determine $g$ this way.

 

[Rosella Lin]

Thank you soooooooooooooooo much ! :) :)