How Can You Calculate the Original Length of a Simple Pendulum?

[John O' Meara]

A simple pendulum of unknown length was found to execute 100 oscillations in 375.6s. The length was then reduced by 50,100,150,200 and 250cm, and the corresponding times of 100 oscillations were found to be 347.7, 317.4,283.9, 245.9 and 200.7: find by calculation the original length of the pendulum?
The only formula I know is T=2(pi)sqr(l/g), I have no idea of how to start. Thanks in advance.I can always plot a graph and find it, but I do not know by calculation.

 

[xman]

You have the right idea, remember that T is the period for one oscillation so we need to divide by time by the number of oscillation and then solve for the length. To check your results plug in the length and try subtracting the given information, and see if you get the new periods when the length is shortened. Hope this helps, sincerely x