from numpy import arange, sin, cos, pi
from matplotlib.pyplot import plot, xlabel, legend, show

def superposition (U1=1.0, U2=1.0, phi=0.0, f=1.0, tmax=4.0, npoints=1000):
    t=arange(npoints)/(npoints-1)*tmax
    u1 = U1*sin(2*pi*f*t)
    u2 = U2*sin(2*pi*f*t+phi)
    plot(t,u1,'--',lw=.75,label='u1')
    plot(t,u2,'--',lw=.75,label='u2')
    plot(t,u1+u2)
    xlabel("t")
    legend()
    show()