1. Second-Order Differential Equations

A series circuit contains a resistor with R = 24 , an inductor with L = 2 H, a capacitor with C = 0.005 F, and a 12 V battery. The initial charge is Q = 0.001 C and the initial current is 0
I have to find the charge at time t

I know how to do the problem if it equaled a function but it just equals 12..i'm confused?

2. Originally Posted by Jessica11
A series circuit contains a resistor with R = 24 , an inductor with L = 2 H, a capacitor with C = 0.005 F, and a 12 V battery. The initial charge is Q = 0.001 C and the initial current is 0
I have to find the charge at time t

I know how to do the problem if it equaled a function but it just equals 12..i'm confused?
You should have a second order linear constant coefficient non-homogeneous ODE for $q$, it is of the form:

$q''+Aq'+Bq=v(t)$

where $v(t)=12$, and $q(0)=0.001$, $q'(0)=0$.

Now this is a bog standard IVP

CB

3. f(x)= 12 is a function! It is a constant function. That just makes this problem easier than if it were a more complicated function.