Question

R = 60, L = 2, C = .0025, E(t) = 100e^-t, I(0) = 0, Q(0) = 0. Find I(t).

Answer 1

LI'(0) + RI(0) + (1/C)*Q(0) = E(0)
2I'(0) + 60I(0) + 400*Q(0) = 100

Answer 2

2I'(0) = 100 -> I'(0) = 50

Answer 3

LI'' + RI' + (1/C)*I = E'(t)
2I'' + 60I' + 400I = E'(t)

Answer 4

2I'' + 60I' + 400I = -100e^-t
2m^2+60m+400=0
m^2+30m+200=0
(m+10)(m+20)=0
m=-10 , -20
Yc=C1e^-10x + C2e^-20x
try to solve for Yp=Ae^x

Answer 5

if Yp=Ae^x what is
Yp'=____? and
Yp''=____?

Answer 6

@ amaes

Answer 7

so that Y(t)= Yc+Yp