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#!/usr/bin/env python
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(theta) + %.2E * cos(theta) + 2e^(%.2f t) (%.2E cos(%.2f t) - %.2E sin(%.2f t))" % (G, B, rer1, reE, imr1, imE, imr1))
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