- #1
thed0ctor
- 11
- 0
I'm reading University Physics 13e by Young and Freedman and we're given this equation:
-L(di/dt)-q/C=0
So we know that i, current, is, i=dq/dt. So the first equation can be read, after some simplification, as
q''+(1/LC)q=0
where q prime means the derivative of q (charge) with respect to time.
This is a homogeneous system so I figure solve it like anything else. So
s^2 = -(1/LC)
=>
s=i*(1/LC)^1/2... the i here is imaginary
let: a=(1/LC)^1/2
thus q=k1*cos(at) + k2*sin(at)
Yet in the formula in the book we end up with the formula:
q=Q*cos(at + phi)
with no sine...
Any help?
-L(di/dt)-q/C=0
So we know that i, current, is, i=dq/dt. So the first equation can be read, after some simplification, as
q''+(1/LC)q=0
where q prime means the derivative of q (charge) with respect to time.
This is a homogeneous system so I figure solve it like anything else. So
s^2 = -(1/LC)
=>
s=i*(1/LC)^1/2... the i here is imaginary
let: a=(1/LC)^1/2
thus q=k1*cos(at) + k2*sin(at)
Yet in the formula in the book we end up with the formula:
q=Q*cos(at + phi)
with no sine...
Any help?