Chapter 7.3, Problem 4P

Program Plan Intro

Program Description: Purpose of problem is to obtain the Laplace transformation of the functions $f\left(t\right)=\cos 2\left(t-\frac{1}{8}\pi \right)e^{-\frac{t}{2}}$ by using translation theorem.

Summary introduction: The translation theorem is defined as if $F\left(s\right)=L\left\{f\left(t\right)\right\}$ exists for $s>c$ , then $L\left\{e^{at}f\left(t\right)\right\}$ exists for $s>a+c$ and $L\left\{f\left(t\right)\right\}=F\left(s\right)\Rightarrow L\left\{e^{at}f\left(t\right)\right\}=F\left(s-a\right)$ .