ode system

from scipy import *
from scipy.integrate import odeint
from matplotlib import *
from pylab import *
"""
Example of solving system of differential equations.
Do the damped oscillator, b is damping factor
"""
def damped_osc(u,t,b): #defines the system of odes
    x=u[0]
    v=u[1]
    return(v,-x-b*v) #the derivatives of u
t = arange(0,20,0.1)
u0 = array([1,0])
b=0.4
u=odeint(damped_osc,u0,t,args=(b,)) #b is in tuple, needs comma
figure(1)    #Using matplotlib
plot(t,u[:,0],t,u[:,1])
xlabel('Time')
title('Damped Oscillator')
figure(2)
plot(u[:,0],u[:,1])
title('Phase-space')
xlabel('Position')
ylabel('Velocity')
show()