How to 3D plot function of 2 variables

I am trying to 3D plot the magnification factor in vibrations for multiple types of damping. To simplify it for those who have no idea what it is, basically, you have 3 variables:

• beta, which varies between 0 and infinite, but I would like to visualize it from 0 to 3, in 0.2 intervals.
• damping ratio, d, which varies between 0 and infinite, but I would like to plot it from 0 to 1, in 0.1 intervals.
• finally, nu, which is a function that varies according to the two variables before.

My intuition says that I should plot this with (X,Y,Z) = (beta, d, nu), but I am just starting to use this library and I am kind of new to python, I just use it when I need to visualize or calculate problems in class. I tried creating 2 arrays for beta and d, but I don't know I should create the array for nu, since it depends on both.

This is the piece of code I have until now:

    import math
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D


nu = []
b = [0.1 + i / 100 for i in range(0, 510)]
damp = [0.1 + i/10 for i in range(0,510)]

for d in damp:
    nu_new = []
    nu.append(nu_new)
    for beta in b:
        nu_new.append( math.sqrt(1+(2*d*beta)**2)/ math.sqrt((1-beta**2)**2+(2*d*beta)**2))

fig = plt.figure()
ax = Axes3D(fig)
ax.plot(b, d, nu)
plt.show()

I am kind of stuck trying to plot this, so if you have any suggestion I would be glad.

This should work: I'm not a Python expert and especially the two for loops might be very unpythonic, but it gets the job done.

import math
import matplotlib.pyplot as plt
import numpy as np

b = np.arange(0.2, 3.2, 0.2)
d = np.arange(0.1, 1.0, 0.1)
nu = np.zeros( (b.size, d.size) )
counter_y = 0

for deta in d:
    counter_x = 0
    for beta in b:
        nu[counter_x, counter_y] = math.sqrt( 1 + (2*deta*beta)**2 ) / math.sqrt( (1-beta**2)**2 + (2*deta*beta)**2)
        counter_x += 1
    counter_y += 1

X, Y = np.meshgrid(d, b)

fig = plt.figure()
ax = fig.add_subplot(111, projection = '3d')
ax.plot_surface(X, Y, nu)