Chapter 7.6, Problem 13P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to obtain the solution $x_{\epsilon }\left(t\right)$ if the initial value problem is $m{x}^{″}=p{d}_{0,\epsilon \left(t\right)};x\left(0\right)=x^{\prime }\left(0\right)=0$ .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that $\underset{\epsilon \to 0}{\lim }{x}_{\epsilon }\left(t\right)$ is the solution of $m{x}^{″}=p\delta \left(t\right);x\left(0\right)=x^{\prime }\left(0\right)=0$ .

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that $mv=p$ if $v=\frac{dx}{dt}$ for $t>0$ .