The differential equations for the charge $q(t)$ in an LRC circuit is

$L{q}^{\text{'}\text{'}}(t)+R{q}^{\text{'}}(t)+\frac{q(t)}{C}=V(t).$

Find the charge and current in an $LRC$ circuit with $L=1H,R=2$Ohm,$C=0\mathrm{.}25F$ and $V=$

$50cos(t)$ volts, if $q(0)=0,C$ and $i(0)=0A.$