Ex.3:

$\alpha=1/(2RC)=0$

a)

$v(t)={I\over {C\omega_0}}\sin(\omega_0 t)$ com $\omega_0 = 1/\sqrt{LC}$;

b)

$i_R(t)=0$; $i_C(t)=I\cos(\omega_0 t)$; $i_L(t)=I[1-\cos(\omega_0 t)]$; gráfico.

$\alpha=1/(2RC) > \omega_0$

a)

$v(t)={I\over {C(r_1-r_2}}(e^{r_1t}-e^{r_2t})$;

b)

$i_R(t)={I\over {RC(r_1-r_2}}(e^{r_1t}-e^{r_2t})$; $i_C(t)={I\over {r_1-r_2}}(r_1e^{r_1t}-r_2e^{r_2t})$; $i_L(t)={I\over {LC(r_1-r_2}}(r_1^{-1}e^{r_1t}-r_2^{-1}e^{r_2t})$;

$\alpha=1/(2RC) = \omega_0$

a)

$v(t)=I/Ct\exp(-\alpha t)$;

b)

$i_R(t)=(I/RC) t \exp(-\alpha t)$;

$i_C(t)=I\exp(-\alpha t) (1-\alpha t)$;

$i_L(t)=I[1-\exp(-\alpha t)(1-\alpha t/2)]$; gráfico.

$\alpha=1/(2RC) < \omega_0$

a)

$v(t)=I/(C\omega_d)\exp(-\alpha t)\sin(\omega_d t)$ com $\omega_d=\sqrt{\omega_0^2 - \alpha^2}$;

b)

$i_R(t)=(I/RC\omega_d) \exp(-\alpha t)\sin(\omega_d t)$;

$i_C(t)=-I/\sin(\phi)\exp(-\alpha t)\sin(\omega_d t-\phi)$ com

$\phi=\arctan(\omega_d/\alpha)$;

$i_L(t)=I\{1-[\exp(-\alpha t)/\sin(\phi)] \sin(\omega_d t -\phi)\}$; gráfico.