Numerical Solution to the Nonlinear Pendulum Equation [ PyMath #6 ]

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Today we are going to calculate the solution to the nonlinear pendulum differential equation, its period time for certain initial displacements, gravitational acceleration and string length. We implement the complete elliptic integral of the first kind into python and approximate the period time to a certain degree. Enjoy :) Video sponsored by Wondershare btw! =)
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The Code:
import math
def elliptic(n,k):
k = math.sin(k *math.pi / 360)
s = 1
for i in range(0, n+1):
p = 1
for j in range(1, 2*i+1+1 , 2):
p *= j / (j+1)
s += (p * k**(i+1))**2
return float(math.pi/2 * s)
l = int(input("String length l? "))
g = float(input("Gravitational acceleration g? "))
phi = float(input("Initial displacement phi_0? "))
n = int(input("Degree of approximation n? "))
print('')
print("Period time T =", 4*math.sqrt(l/g)*elliptic(n, phi))
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