An experiment to measure the acceleration due to gravity g of a pendulum is done. The length of threads l/m are 0.35, 0.65, 1.00, 1.45, 1.95 &...

I like to do this a different way, although we get the
same result.

Start with T = 2 * pi *
sqrt(L/g)

Solve for g:  g = (4 * pi^2 *
L)/(T/20)^2

I hope you can read my notation.  The factor of
T/20 is because we are given the period of 20
oscillations.

Substituting our data for L and T, we
get

L           T          
g

0.35      24.1     
9.52

0.65      32.4     
9.78

1.00      40.1     
9.82

1.45      47.5     
10.15

1.95      56.3     
9.71

The value of 10.15 is probably an outlier that we
could discard, but what the hey.  The average value for g
is

g = 9.80 m/s^2, in good agreement with the
textbooks.

Comparing with the previous
response:

His value for g = pi^2 = 9.87.  I think his
answer is different because he simplified, considering only the data for L= 1 and T/20 =
2.

Incidentally, I did all the arithmetic with Excel, the
poor man's mathematical analyser.