Measuring Gravity with a Pendulum.

fiz.py

import numpy as np
import pandas as pd

df = pd.read_csv('grav.csv')
pd.set_option('display.width', 1000)

def t_avg(row):
    return sum(row[0:4]) / 4

df['t_avg'] = df.apply(lambda row: t_avg(row), axis=1)

def t_err(row):
    t_max = max(row[0:4]); t_min = min(row[0:4])
    return (t_max - t_min) / 2

df['t_err'] = df.apply(lambda row: t_err(row), axis=1)

def l_avg(row):
    return sum(row[4:7]) / 3

df['l_avg'] = df.apply(lambda row: l_avg(row), axis=1)

def l_err(row):
    l_max = max(row[4:7]); l_min = min(row[4:7])
    return (l_max - l_min) / 2

df['l_err'] = df.apply(lambda row: l_err(row), axis=1)

def g_avg(row):
    L = (row['l_avg'] + 1) / 100
    T = row['t_avg'] / 10
    return (4 * ((3.14) ** 2) * L) / (T ** 2)

df['g_avg'] = df.apply(lambda row: g_avg(row), axis=1)

def g_err(row):
    L = (row['l_avg'] + 1) / 100
    L_err = row['l_err'] / 100
    T = row['t_avg'] / 10
    T_err = row['t_err'] / 10
    return row['g_avg'] * ((L_err / L) + 2 * (T_err / T))

df['g_err'] = df.apply(lambda row: g_err(row), axis=1)

g = sum(df['g_avg']) / 3; g_err = sum(df['g_err']) / 3
p = sum(df['g_avg'][1:]) / 2; p_err = sum(df['g_err'][1:]) / 2

print df
print "=== RESULT ==="
print "g = {0} +- {1} m/s^2".format(g, g_err)
print "g = {0} +- {1} m/s^2 (optimal)".format(p, p_err)

grav.csv

      t0     t1     t2     t3   l0   l1   l2    t_avg  t_err       l_avg  l_err     g_avg     g_err
0  20.40  20.48  20.11  20.55   98  101   99  20.3850  0.220   99.333333    1.5  9.522327  0.347895
1  24.77  24.72  24.72  24.41  149  151  150  24.6550  0.180  150.000000    1.0  9.796845  0.207928
2  28.56  28.52  28.57  28.48  201  198  201  28.5325  0.045  200.000000    1.5  9.737236  0.103380
=== RESULT ===
g = 9.68546923148 +- 0.219734502545 m/s^2
g = 9.76704028632 +- 0.155654240402 m/s^2 (optimal)

Location: Szczecin, Poland