Answer
$i(t) = 3.8*cos(3t - 0.31804) A$
Work Step by Step
Start by finding the equivalent impedance circuit by taking the series impedance of the three components in phasor notation
$Z_{series}(\omega j) = 3 + 3*\omega e^{j*\pi/2} - \frac{1}{3\omega} e^{j*\pi /2} $
$V(3j) = 12$
Find current using ohms law
$\frac{V(3j)}{Z(3j)} = \frac{12}{3+ \frac{80}{81}e^{j \pi/2}} $
Use a calculator with complex capabilities to simplify the equation or multiply by the complex conjugate and simplify to the current
$i(t) = 3.8*cos(3t - 0.31804) A$
