plot 2 branches archimedean spiral in python

[ALosh99]

I plot the archimedaen spirlas for one branch, how can I plot more than one branches starting from the original, my code that I have written :

n= 1000
a= 2.     # will turn the spiral
v= 1
omega = 0.1
r0 = v/omega
T=100
N=10000
t=np.linspace(0,T,N+1)
r= v*t
theta = a + r/r0
dt=float(T)/N 
x=r* np.cos(theta) 
y=r* np.sin(theta)
plt.plot(x,y)
plt.show()