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3.3.1 - I'' + RI'/L + I/LC = F/L cos wt - Coggle Diagram
3.3.1 - I'' + RI'/L + I/LC = F/L cos wt
Electric circuit
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
Solutions to Second Order Differential Equations
Variation of parameters
yp(t) = c1(t) y1(t) + c2(t) y2(t)
Wronskian
Laplace Transform
Transform of f(t) = integral 0 to infinite of f(t) * exp(-st)
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
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
