I have another RLC Circuit questions where L = 2.0H, R = 1.5 ohms and C = 0.2 F. The impressed voltage is E(t) = 20 sin 3t V.

I got a general solution for the D.E. as:

$\displaystyle Q = e^{-\frac{3}{8} t} (c_{1} cos (\frac{\sqrt{151}}{8} t) + c_{2} sin (\frac{\sqrt{151}}{8} t) - \frac{40}{757}(9 cos 3t + 26 sin 3t)$

Using the initial conditions given ( Q(0) = 2.5C and I(0) = OA) I calculated the current as:

$\displaystyle I(t) = -\frac{\sqrt{151}}{8} e^{-\frac{3}{8} t} ( \frac{23880}{114307} cos (\frac{\sqrt{151}}{8} t) + \frac{360}{757} sin (\frac{\sqrt{151}}{8} t)) - \frac{3}{8} e^{-\frac{3}{8} t} (\frac{360}{757} cos (\frac{\sqrt{151}}{8} t - \frac{23880}{114307} sin (\frac{\sqrt{151}}{8} t)) - \frac{40}{757}(27 sin 3t - 78 sin 3t)$

This just seems so messy. Can anyone help to confirm the answer or show me where I have gone wrong?