Pendulum

#!/usr/bin/python2

# script for solving g from pendulum experiment ( http://physics.stackexchange.com/q/106531/43812 )
# - LENGTH => length of the string
# - g => constant (used for solving T - not needed, just a test)
# - data => data obtained from the experiment - [[T_0,alpha_0],[T_1,alpha_1],..]
# - PRECISION => precision of the sum, since we can't count to infinity (yet)

# Output for this setup:
# Running test
# Average T: 1.18953233488
# Average g: 9.40189803166

from math import *

LENGTH = 0.31
G = 9.81
data=[[1.15, 11.54], [1.16, 26.57], [1.18, 39.49], [1.18, 44.11], [1.2, 52.15], [1.22, 58.29], [1.23, 63.96], [1.25, 66.53], [1.28, 73.78], [1.3, 83.54]]
PRECISION = 80

SUM = lambda alpha:sum([(factorial(2.*n) / (2.**n*factorial(n))**2 )**2 * sin(radians(alpha)/2)**(2*n) for n in xrange(PRECISION)])
t = lambda alpha, length=LENGTH, g=G: 2.*pi*sqrt(length/g)*SUM(alpha)
g = lambda alpha, period, length=LENGTH: ((2*pi*SUM(alpha))/(period))**2 * length


if __name__=="__main__":
    print("Running test")
    all_t=[ t(i[1]) for i in data ]
    print("Average T: {0}".format(sum(all_t)/len(all_t)))
    all_g=[ g(i[1],i[0]) for i in data ]
    print("Average g: {0}".format(sum(all_g)/len(all_g)))