3.3.1 - I'' + RI'/L + I/LC = F/L cos wt
Electric circuit
Solutions to Second Order Differential Equations
Variation of parameters
Laplace Transform
Undetermined Coefficients
f(t) = exponential exp(st), y(t) = Y exp(st)
f(t) = Acos wt + Bsin wt, y(t) = MCos wt + NSin wt
f(t) = polynomial t, y(t) = polynomial t
yp(t) = c1(t) y1(t) + c2(t) y2(t)
Wronskian
Transform of f(t) = integral 0 to infinite of f(t) * exp(-st)
Damping
Overdamping
R > 2 sqrt(L/C)
2 Real Roots
Critical damping
R = 2 sqrt(L/C)
2 Equal Real Roots
Underdamping
R < 2 sqrt(L/C)
2 Complex Roots
No damping
R = 0
2 Real Roots
R = Resistor, C = Capacitor, L = Inductor
Series
Series RL Circuit
Series RC Circuit
Series RLC Circuit 
Series LC Circuit
Parallel
Parallel RL Circuit
Parallel RC Circuit
Parallel RLC Circuit
Parallel LC Circuit