1. Given
+
Vs
i(t)
t=0
R
L
+
C
v(t)
Figure 2.1: Step voltage applied to a series RLC circuit.
(a) Verify that the differential equation for $v(t)$ is found as
$\frac{d^2v}{dt^2} + \frac{R}{L}\frac{dv}{dt} + \frac{v}{LC} = \frac{V_s}{LC}$
(b) If $v(0^-) = -5V$ and $i(0^-) = 0A$, find the voltage response, $v(t)$, for $t > 0$ when
$V_s = 5V$, $R = 330\Omega$, $L = 100mH$, $C = 0.1\mu F$