A pendulum simulation using fourth order Runge-Kutta integration

pend_4rk.py

from scipy import *
from matplotlib.pyplot import *
##A pendulum simulation using fourth order 
##Runge-Kutta integration
##v0.1
##Alexandros Kourkoulas Chondrorizos

ts=.05 #time step size
td=40 #trial duration
te=int(td/ts) #no of timesteps

mu=0.1 #friction factor
m=1 #mass
g=9.81 #grav. acceleration
l=1 #length

th=[pi/4]#((rand()*2)-1)*pi] #initial angle
om=[0] #initial angular velocity
u=0 #torque

for j in range(te):
    #Euler approximation
    th.append(th[j] + ts*om[j])
    f1 = (-mu*om[j] + m*g*l*sin(th[j]) + u)/(m*(l^2))
    om.append(om[j] + ts*f1)
    
    #approximation 1 at mid-interval
    th2 = th[j+1] + (ts/2)*om[j+1]
    f2 = (-mu*om[j+1] + m*g*l*sin(th[j+1]) + u)/(m*(l^2))
    om2 = om[j+1] + (ts/2)*f2
    
    #approximation 2 at mid-interval
    th3 = th2 + (ts/2)*om2
    f3 = (-mu*om2 + m*g*l*sin(th2) + u)/( m*(l^2))
    om3 = om2 + (ts/2)*f3
    
    #approximation at next time step
    th4 = th3 + (ts)*om3
    f4 = (-mu*om3 + m*g*l*sin(th3) + u)/( m*(l^2))
    om4 = om3 + (ts)*f4
    
    dth=(om[j] + 2*om[j+1] + 2*om2 + om3)/6
    dom=(f1 + 2*f2 + 2*f3 + f4)/6
    th[j+1] = th[j] + ts*dth
    om[j+1] = om[j] + ts*dom
    
subplot(211),plot(th),xlabel('Angle'),ylabel('')
subplot(212),plot(om,'r'),xlabel('Angular velocity'),ylabel('')
show()

Something with the plot(?) seems to be wrong, please correct me if I interpret it incorrectly:
If I run this example, the angle-plot seemingly fades out to Pi, but shouldn't it be 0?
"Angle" refers to the deflection of the pendulum from its idle-position, doesn't it?
And indeed, if I replace the initial angle of Pi/4 by 0, i.e. idle position the pendulum resides there, giving a constant-0 angle plot.
So, is Pi equivalent to 0 here? I would interpret 2Pi as the next-period idle position (a full turn), or is the pendulum Pi-periodic? Or is there some bug?
Is there an initial angle that will let the pendulum end up at 0?

@Stewori
In this script, an angle of 0 is chosen to be at the top (yes, it is more convenient to choose 0 at the bottom, but this works too)

The reason why choosing an initial angle of 0 yields a constant-0 angle plot is that it can stand exactly upright without movement, try choosing 0.00001 and you'll see it fall down to pi eventually.