Question

in problems 1-20find either f(S)or f(t),as indicated${\mathit{L}}^{\mathbf{-}\mathbf{1}}\frac{\mathbf{1}}{{\mathbf{s}}^{\mathbf{2}}\mathbf{-}\mathbf{6}\mathbf{s}\mathbf{+}\mathbf{10}}$

Short answer

find either f(S)or f(t),as indicated

$\begin{array}{l}f\left(t\right)=L^{-1}\frac{1}{s^2-6s+9+1}\\ L^{-1}\frac{1}{{\left(s-3\right)}^2+1^2}\end{array}$

Step-by-step solution

Step 1: Definition of indicated

The definition of indicate is to refer to, point to, or show something, or to make a brief statement acknowledging something. When you point to Susie, you are indicating.

Now,

$\begin{array}{l}f\left(t\right)=L^{-1}\frac{1}{s^2-6s+9+1}\\ L^{-1}\frac{1}{{\left(s-3\right)}^2+1^2}\end{array}$

$L^{-1}\frac{1}{{\displaystyle {\overline{)s^2+1^2}}_{s\to s-3}}}$$L^{-1}\left\{F(s-a)\right\}=L^{-1}$${\overline{)F\left(S\right)}}_{s\to s-3}==e^{at}f\left(t\right)=L^{-1}$

find the value of  f(t).

$$\begin{gathered} \frac{b}{s^2+b^2}=\sin bt \\ =e^{3t}\sin t \\ f\left(t\right)=e^{3t}\sin t \end{gathered}$$

Hence, the value is $f\left(t\right)=e^{3t}\sin t$