$(30$ points$)$ In an L$-$C circuit, L$=80\mathrm{.}12$mH and C$=3\mathrm{.}09\backslash$mu F and the

two devices are connected in series. During oscillations of the circuit,

the maximum charge on the capacitor plates is $4\mathrm{.}17\backslash$times $10^(-7)$C$=0\mathrm{.}417\backslash$mu C$.$

$($a$)(15$ points$)$ Find the magnitude Q of the charge on the capacitor at

an instant when the current has a magnitude equal to one$-$fourth the

maximum current.

$($b$)(5$ points$)$ What is the period T of the oscillation?

$($c$)(10$ points$)$ Assume the capacitor had the maximum charge at time t

$=0.$ Find the charge Q when t$=($T$)/(6),$ where T is the period.