Laplace Transform Theories

Given  $g\left(t\right)=e^{5t}f\left(t\right)$  , what is G(s)?

•  $G\left(s\right)=F\left(s-5\right)$  

•  $G\left(s\right)=\left(-1\right)^5\frac{\text{d}^5F\left(s\right)}{\text{d}s^5}$  

•  $G\left(s\right)=F\left(s+5\right)$  

•  $G\left(s\right)=\left(-1\right)^4\frac{\text{d}^4F\left(s\right)}{\text{d}s^4}$  

Given  $g\left(t\right)=t^3f\left(t\right)$  , what is G(s)?

•  $G\left(s\right)=F\left(s-3\right)$  

•  $G\left(s\right)=\left(-1\right)^3\frac{\text{d}^3F\left(s\right)}{\text{d}s^3}$  

•  $G\left(s\right)=F\left(s+3\right)$  

•  $G\left(s\right)=\left(-1\right)^2\frac{\text{d}^2F\left(s\right)}{\text{d}s^2}$  

Given  $g\left(t\right)=\frac{f\left(t\right)}{t}$  , what is G(s)?

•  $G\left(s\right)=\int_s^{\infty}F\left(u\right)du$  

•  $G\left(s\right)=\left(-1\right)\frac{\text{d}F\left(s\right)}{\text{d}s}$  

•  $G\left(s\right)=\int_{\infty}^sF\left(u\right)du$  

•  $G\left(s\right)=^{\left(-1\right)^{-1}}\frac{\text{d}F\left(s\right)}{\text{d}s}$  

Given  $g\left(t\right)=e^{10t}\ \ \sin5t$  . Which function is selected to be transformed into s-domain first?

•  $\sin\ 5t$  

•  $e^{10t}$  

Given  $g\left(t\right)=e^{7t}\ \ \cosh2t$  . Which function is selected to be transformed into s-domain first?

•  $\cosh2t$  

•  $e^{7t}$  

Given  $g\left(t\right)=t^2\ \ \cos3t$  . Which function is selected to be transformed into s-domain first?

•  $\cos3t$  

•  $t^2$  

Given  $g\left(t\right)=\frac{\cos3t}{t}$  . Which function is selected to be transformed into s-domain first?

•  $\cos3t$  

•  $t$  

•  $\frac{1}{t}$  

Given  $g\left(t\right)=e^{8t}\ \left(\frac{1}{t}\right)$  . Which function is selected to be transformed into s-domain first?

•  $e^{8t}$  

•  $t$  

•  $\frac{1}{t}$  

Given  $g\left(t\right)=t^{10}\ \ e^{8t}$  . Which function is selected to be transformed into s-domain first?

•  $e^{8t}$  

•  $t^{10}$  

Given  $g\left(t\right)=f'''$  , what is G(s)?

•  $G\left(s\right)=s^3\ F\left(s\right)-s^2f\left(0\right)-sf'\left(0\right)-f''\left(0\right)$  

•  $G\left(s\right)=s^3\ F\left(s\right)+s^2f\left(0\right)+sf'\left(0\right)+f''\left(0\right)$  

•  $G\left(s\right)=s^3f\left(0\right)-s^2f'\left(0\right)-sf''\left(0\right)-f'''\left(0\right)$  

•  $G\left(s\right)=s^3f\left(0\right)+s^2f'\left(0\right)+sf''\left(0\right)+f'''\left(0\right)$