Determine the Laplace transform of each of the following

Chapter 7, Problem 31E

(choose chapter or problem)

Determine the Laplace transform of each of the following functions:

(a) \(f_{1}(t)=\left\{\begin{array}{l}

0 \\

\end{array}\right.

\) \(\begin{aligned}

&t=2 \\

&t \neq 2

\end{aligned}

(b) $f_{2}(t)= \begin{cases}5, & t=1, \\ 2, & t=6, \\ t, & t \neq 1,6\end{cases}$

Which of the preceding functions is the inverse Laplace transform of 1/ ${s}^{2}$ ?

Equation transcription:

${f}_{1}(t)=\{{\ }_{t,}^{0,}$

${\ }_{t\ne{}2,}^{t=2,}$

${f}_{2}(t)=\{{\ }_{\ \ t,\ \ \ \ \ \ \ \ \ \ \ \ \ \ t\ne{}1,6,}^{{\ }_{2,}^{5,}\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\ }_{t=6,}^{t=1,}}$

${f}_{3}(t)=t$

Text transcription:

f_{1}(t)=\left\{\begin{array}{l}

0 \\

\end{array}\right.

\begin{aligned}

&t=2 \\

&t \neq 2

\end{aligned}

f_{2}(t)= \begin{cases}5, & t=1, \\ 2, & t=6, \\ t, & t \neq 1,6\end{cases}

f_{3}(t)=t

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