Chapter 7.6, Problem 19P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the $LC$ circuit is defined by the differential equation $i^{″}+100i=10{\displaystyle \sum _{n=0}^{\infty }{\left(-1\right)}^n\delta \left(t-\frac{n\pi }{10}\right)};i\left(0\right)=i^{\prime }\left(0\right)=0$ .

(b)

Program Plan Intro

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

  $i^{″}+100i=10{\displaystyle \sum _{n=0}^{\infty }{\left(-1\right)}^n\delta \left(t-\frac{n\pi }{10}\right)};i\left(0\right)=i^{\prime }\left(0\right)=0$ and show $i\left(t\right)=\left(n+1\right)\sin 10t$ if $\frac{n\pi }{10}<t<\frac{\left(n+1\right)\pi }{10}$ .