$[2\mathrm{.}5/5$ Points$]$

ZILLDIFFEQ$97\mathrm{.}3\mathrm{.}034.$

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Recall that the differential equation for the instantaneous charge $q(t)$ on the capacitor in an LRC$-$series circuit is

$L\frac{d^{2}q}{d{t}^2}+R\frac{dq}{dt}+\frac{1}{c}q=E(t)$

See this excerpt about $\frac{?}{{?}_{R}C}-$series circuits. Use the Laplace transform to find $q(t)$ when $L=1h,R=20,C=0\mathrm{.}005f,E(t)=160V,t>0,q(0)=0,$ and $i(0)=0.$

$q(t)=$

What is the current $i(t)?$

$i(t)=$

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