(Solved): Consider a single-loop circuit containing an inductor, resistor, and ca- pacitor. Let q(t) d ...

• Consider a single-loop circuit containing an inductor, resistor, and ca-
pacitor. Let q(t) denote the charge on a capacitor and E(t) impressed
voltage on the loop, respectively. Let also the constants L, R and C
denote inductance, resistance and capacitance, respectively. The model
describing the relationship between g(t) and E(t) is
d²q
L +
dt²
1
+79=E(t).
Suppose L = 1, C = 0.5, R = 3 and E(t) = t² + 1. Find the charge
on the capacitor when t = 2, given that q(0) = 1 and g(1) = 4.

- Consider a single-loop circuit containing an inductor, resistor, and capacitor. Let $q(t)$ denote the charge on a capacitor and $E(t)$ impressed volt age on the loop, respectively. Let also the constants $L,R$ and $C$ denote inductance, resist ance and capacit ance, respectively. The model describing the relationship between $q(t)$ and $E(t)$ is $L\frac{d^{2}q}{d{t}^2}+R\frac{dq}{dt}+\frac{1}{C}q=E(t)$ Suppose $L=1,C=0.5,R=3$ and $E(t)=t^2+1$. Find the charge on the capacitor when $t=2$, given that $q(0)=1$ and $q(1)=4$.