Chapter 7.6, Problem 18P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the circuit is defined by the differential equation $L{i}^{″}+\frac{1}{C}i=e_0\delta \left(t\right)-e_0\delta \left(t-a\right);i\left(0\right)=i^{\prime }\left(0\right)=0$ .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to solve the differential equation

$L{i}^{″}+\frac{1}{C}i=e_0\delta \left(t\right)-e_0\delta \left(t-a\right);i\left(0\right)=i^{\prime }\left(0\right)=0$ for given conditions, and show $i\left(t\right)=\sin 10t$ if $t<\pi$ and $i\left(t\right)=0$ if $t>\pi$ .