An LRC circuit is set up with an inductance of $\frac{1}{6}$ henry, a resistance of $1$ohm, and a capacitance of $\frac{6}{5}$ farad. Assuming the initial

charge is $5$ coulombs and the initial current is $3$ amperes, find the solution function describing the charge on the capacitor at any time.

What is the charge on the capacitor after a long period of time?

Write the function that describes the charge on the capacitor at any time.

$q(t)=$

$($Type an exact answer.$)$