# Find the charge in the steady state. What does steady state mean in this problem?

A voltage $E(t)$ is applied to a RCL Circuit connected in series. The charge on the capacitor at any time, $t$ in seconds is given by :

$$q’’ + 9 q’ + 14 q =E(t) = \frac{1}{2} \sin t$$

Given that there is no initial charge, but an initial current of $1$ amperem what is the charge in the steady state ?

First, I solved this differential equation using Laplace transform and got

$$q(t) = \frac{1}{500} (110 e^{-7t} - 101e^{-7t} + 13 \sin t - 9 \cos t)$$

What does steady state mean ?

Why is the answer for the charge in steady charge $q(t) = \frac{1}{500} (13 \sin t - 9 \cos t )$ (Without the part that I’ve taken out.)

• Your solution doesn't include $E(t)$ in any way- it should, shouldn't it? – Brian Borchers Aug 20 '18 at 12:12
• Yes, I’ve updated it. The E(t) was originally there and I was told that e(t) is $1/2 \sin t$ so that I can find $q(t)$ – user185692 Aug 20 '18 at 12:15
• I would assume "steady state" means the state that the system eventually settles in, i.e. as $t\gg 0$. – Arthur Aug 20 '18 at 12:16