added multiple curves, demonstrating fundamental error

1 files changed, 40 insertions, 41 deletions

diff --git a/graph.py b/graph.py
index 8b66af7..5c1bbb5 100644
--- a/graph.py
+++ b/graph.py
@@ -4,47 +4,46 @@ import matplotlib.pyplot as plt
 import tkinter
 from math import sin,cos,e
 
-w = 100 # May vary
-c1 = 2.5*10**(-6)
-c2 = 1*10**(-6)
-r1 = 200
-rload = 1000
-
-a = 1
-b = c1*r1*rload + r1*c2*rload + (rload**2)*c2
-c = rload
-
-det = (b**2-4*a*c)**(1/2)
-r1 = (-b-det)/(2*a)
-r2 = (-b+det)/(2*a)
-
-A = c1*c2*rload**2*w*(rload-w**2)/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4)
-B = b*c1*c2*rload**2*w**3/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4)
-C = - c1*c2*rload**2*w*(rload-w**2)/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4)
-D = - b*c1*c2*rload**3*w/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4) # from https://www.wolframalpha.com/input/?i=solve+for+x1%2Cx2%2Cx3%2Cx4+in+%7B%7B1%2C0%2C1%2C0%7D%2C+%7Bb%2C1%2C0%2C1%7D%2C+%7BR%2C+b%2C+w%5E2%2C+0%7D%2C+%7B0%2C+R%2C+0%2C+w%5E2%7D%7D*%7Bx1%2Cx2%2Cx3%2Cx4%7D+%3D+%7B0%2C0%2Cw*c_1*c_2*R%5E2%2C0%7D and an insane partial fraction decomposition
-E = (D-C*r1)/(r2-r1)
-F = C - E # Another PFD of Cs-D/(as^2+bs+c)
-G = B/w
-
-# Final solution should be
-# Gsin(theta) + Bcos(theta) + Ee^(r1 t) + Fe^(r2 t)
-# But E, F, r1, and r2 are complex. Luckily, conjugates make it that
-# = 2e^(Re(r1) t) ( Re(E)cos(Im(r1)t) - Im(E)sin(Im(r1)t) )
-rer1 = r2.real
-reE = F.real
-imr1 = r2.imag
-imE = F.imag # switched because positive ones were needed
-
-print("%.2E * sin(t) + %.2E * cos(t) + 2e^(%.2f t) (%.2E cos(%.2f t) - %.2E sin(%.2f t))" % (G, B, rer1, reE, imr1, imE, imr1))
-
 def f(x):
     return G*sin(x) + B*cos(x) + 2*e**(rer1 * x) * (reE * cos(imr1 * x) - imE * sin(imr1 * x))
-
-x = []
-y = []
-for i in range(0, 1000):
-    x.append(i/100)
-    y.append(f(i/100))
-
-plt.plot(x,y)
+for w in range(100,10000,100):
+    c1 = 2.5*10**(-6)
+    c2 = 1*10**(-6)
+    r1 = 200
+    rload = 1000
+
+    a = 1
+    b = c1*r1*rload + r1*c2*rload + (rload**2)*c2
+    c = rload
+
+    det = (b**2-4*a*c)**(1/2)
+    r1 = (-b-det)/(2*a)
+    r2 = (-b+det)/(2*a)
+
+    A = c1*c2*rload**2*w*(rload-w**2)/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4)
+    B = b*c1*c2*rload**2*w**3/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4)
+    C = - c1*c2*rload**2*w*(rload-w**2)/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4)
+    D = - b*c1*c2*rload**3*w/(b**2*w**2 + rload**2 - 2*rload*w**2 + w**4) # from https://www.wolframalpha.com/input/?i=solve+for+x1%2Cx2%2Cx3%2Cx4+in+%7B%7B1%2C0%2C1%2C0%7D%2C+%7Bb%2C1%2C0%2C1%7D%2C+%7BR%2C+b%2C+w%5E2%2C+0%7D%2C+%7B0%2C+R%2C+0%2C+w%5E2%7D%7D*%7Bx1%2Cx2%2Cx3%2Cx4%7D+%3D+%7B0%2C0%2Cw*c_1*c_2*R%5E2%2C0%7D and an insane partial fraction decomposition
+    E = (D-C*r1)/(r2-r1)
+    F = C - E # Another PFD of Cs-D/(as^2+bs+c)
+    G = B/w
+
+    # Final solution should be
+    # Gsin(theta) + Bcos(theta) + Ee^(r1 t) + Fe^(r2 t)
+    # But E, F, r1, and r2 are complex. Luckily, conjugates make it that
+    # = 2e^(Re(r1) t) ( Re(E)cos(Im(r1)t) - Im(E)sin(Im(r1)t) )
+    rer1 = r2.real
+    reE = F.real
+    imr1 = r2.imag
+    imE = F.imag # switched because positive ones were needed
+
+    print("%.2E * sin(t) + %.2E * cos(t) + 2e^(%.2f t) (%.2E cos(%.2f t) - %.2E sin(%.2f t))" % (G, B, rer1, reE, imr1, imE, imr1))
+
+    x = []
+    y = []
+    for i in range(1000):
+        x.append(i/100)
+        y.append(f(i/100))
+
+    plt.plot(x,y)
 plt.show()