A Series Circuit Consists of a Resistor $R = 32 \Omega$

Multiple Choice

A series circuit consists of a resistor $R = 32 \Omega$ , an inductor with $L = 4 H$ , a capacitor with $C = 0.003125 \mathrm {~F}$ , and a $24$ -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.

A) $I ( t ) = 0.742 e ^ { - 4 t } \sin ( 8 t )$
B) $I ( t ) = \frac { e ^ { - 4 t } } { 160 } \cos ( 8 t )$
C) $I ( t ) = \frac { e ^ { - 4 t } } { 160 } \cos ( 8 t ) - \frac { 1 } { 2 }$
D) $I ( t ) = 0.742 e ^ { - 8 t }$
E) $I ( t ) = \frac { e ^ { - 4 t } } { 160 } ( 0.003125 \cos ( 4 t ) + 8 \sin ( 4 t ) ) - \frac { 1 } { 2 }$