I am doing a pendulum project for algebra 2. I am trying to find the theoretical period. The length of the pendulum is 30 CM. The experimental period is 0.863666. The formula that I was told to use is L=980t^2/4pi^2. This represents the length of a simple pendulum with a period of t seconds. In this formula the acceleration due to gravity is given as 980cm/s^2. I need to solve for t and I have to use the formula to find the theoretical period. I'm really confused about this...please help? Thanks in advance!

Question

anonymous · Answer

You need to solve:
$$L=\frac{980 t^2}{4 \pi^2} \implies t^2 = \frac{4 \pi^2}{980}L \implies t=\sqrt{\frac{4 \pi^2}{980}L}= 2 \pi \sqrt{\frac{L}{980}}$$
The length is given in centimeters so the units would be:
$$\sqrt{\frac{[\textrm{cm}]}{[\textrm{cm}][\textrm{s}^{-2}]}}=[\textrm{s}]$$
The unit of a period, as expected.

anonymous · Answer

Does that make sense? Always check your units when doing anything other than pure math. You can catch algebra mistakes easily if the units don't make sense. For example, if you are expecting a distance, you should get meters (or cm, mm, etc.)

anonymous · Answer

So since my experimental period is 0.863666 and I know my length is 30 cm do I just plug in those numbers to that equation?

anonymous · Answer

Well you want the period, that is t. So you only need plug in the length (30 cm) and run it through a calculator.

anonymous · Answer

Okay! I was getting confused thinking the experimental period had something to do with the equation! Thank you so much for helping! (=