Chapter 7.1, Problem 17P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform of the given function $f\left(t\right)={\cos }^{2}2t$ .

Summary introduction:Program will use the Laplace transform as given below.

  $\begin{array}{l}L\left\{\cos kt\right\}=\frac{s}{s^2+k^2}\\ L\left\{1\right\}=\frac{1}{s}\end{array}$

Here, the value of $s>0$ .

The linearity theorem of the Laplace transform for all $s$ such that the functions $f$ and $g$ both exists is defined as,

  $L\left\{af\left(t\right)+bg\left(t\right)\right\}=aL\left\{f\left(t\right)\right\}+bL\left\{g\left(t\right)\right\}$