Chapter 7.6, Problem 21P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to show that current in the $RLC$ circuit is defined by the differential equation $i^{″}+60i^{\prime }+1000i=10{\displaystyle \sum _{n=0}^{\infty }{\left(-1\right)}^n\delta \left(t-\frac{n\pi }{10}\right)};i\left(0\right)=i^{\prime }\left(0\right)=0$ .

(b)

Program Plan Intro

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

  $i^{″}+60i^{\prime }+1000i=10{\displaystyle \sum _{n=0}^{\infty }{\left(-1\right)}^n\delta \left(t-\frac{n\pi }{10}\right)};i\left(0\right)=i^{\prime }\left(0\right)=0$ and show $i\left(t\right)=\frac{e^{3n\pi +3\pi }-1}{e^{3\pi }-1}{e}^{-30t}\sin 10t$ if $\frac{n\pi }{10}<t<\frac{\left(n+1\right)\pi }{10}$ .